Characterizations of the metric and generalized metric projections on subspaces of Banach spaces

The variational principles of the metric projection onto closed and convex sets are commonly used as the basis for characterizations of metric projections onto subspaces of Hilbert spaces. However, it is important to realize that the variational principles do not hold as necessary and sufficient con...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Khan, Akhtar A. [verfasserIn] Li, Jinlu [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Generalized projection Generalized metric projection Generalized proximal set Generalized Chebyshev set Generalized identical points Orthogonal subspaces

Übergeordnetes Werk:	Enthalten in: Journal of mathematical analysis and applications - Amsterdam [u.a.] : Elsevier, 1960, 531
Übergeordnetes Werk:	volume:531

DOI / URN:	10.1016/j.jmaa.2023.127865

Katalog-ID:	ELV065689089

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520			\|a The variational principles of the metric projection onto closed and convex sets are commonly used as the basis for characterizations of metric projections onto subspaces of Hilbert spaces. However, it is important to realize that the variational principles do not hold as necessary and sufficient conditions in general Banach spaces to characterize the metric projection and its related extensions. This technical handicap prevents the study of metric projection onto subspaces of general Banach spaces from being fully explored. Motivated by this existing lacuna in the literature, we investigate the metric projection and the generalized metric projection onto subspaces of general Banach spaces in this study. Focusing on concrete Banach spaces, we show that even though there are no general variational principles in such spaces for the projection onto subspaces, specific elements satisfy a variational characterization. We provide concrete examples to illustrate various notions of projections in general Banach spaces.
650		4	\|a Generalized projection
650		4	\|a Generalized metric projection
650		4	\|a Generalized proximal set
650		4	\|a Generalized Chebyshev set
650		4	\|a Generalized identical points
650		4	\|a Orthogonal subspaces
700	1		\|a Li, Jinlu \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Journal of mathematical analysis and applications \|d Amsterdam [u.a.] : Elsevier, 1960 \|g 531 \|h Online-Ressource \|w (DE-627)266886922 \|w (DE-600)1468566-8 \|w (DE-576)103373101 \|x 1096-0813 \|7 nnns
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Indexfelder

author_variant	a a k aa aak j l jl
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bklnumber	31.00
publishDate	2023
allfields	10.1016/j.jmaa.2023.127865 doi (DE-627)ELV065689089 (ELSEVIER)S0022-247X(23)00868-5 DE-627 ger DE-627 rda eng 510 VZ 31.00 bkl Khan, Akhtar A. verfasserin aut Characterizations of the metric and generalized metric projections on subspaces of Banach spaces 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The variational principles of the metric projection onto closed and convex sets are commonly used as the basis for characterizations of metric projections onto subspaces of Hilbert spaces. However, it is important to realize that the variational principles do not hold as necessary and sufficient conditions in general Banach spaces to characterize the metric projection and its related extensions. This technical handicap prevents the study of metric projection onto subspaces of general Banach spaces from being fully explored. Motivated by this existing lacuna in the literature, we investigate the metric projection and the generalized metric projection onto subspaces of general Banach spaces in this study. Focusing on concrete Banach spaces, we show that even though there are no general variational principles in such spaces for the projection onto subspaces, specific elements satisfy a variational characterization. We provide concrete examples to illustrate various notions of projections in general Banach spaces. Generalized projection Generalized metric projection Generalized proximal set Generalized Chebyshev set Generalized identical points Orthogonal subspaces Li, Jinlu verfasserin aut Enthalten in Journal of mathematical analysis and applications Amsterdam [u.a.] : Elsevier, 1960 531 Online-Ressource (DE-627)266886922 (DE-600)1468566-8 (DE-576)103373101 1096-0813 nnns volume:531 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines VZ AR 531
spelling	10.1016/j.jmaa.2023.127865 doi (DE-627)ELV065689089 (ELSEVIER)S0022-247X(23)00868-5 DE-627 ger DE-627 rda eng 510 VZ 31.00 bkl Khan, Akhtar A. verfasserin aut Characterizations of the metric and generalized metric projections on subspaces of Banach spaces 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The variational principles of the metric projection onto closed and convex sets are commonly used as the basis for characterizations of metric projections onto subspaces of Hilbert spaces. However, it is important to realize that the variational principles do not hold as necessary and sufficient conditions in general Banach spaces to characterize the metric projection and its related extensions. This technical handicap prevents the study of metric projection onto subspaces of general Banach spaces from being fully explored. Motivated by this existing lacuna in the literature, we investigate the metric projection and the generalized metric projection onto subspaces of general Banach spaces in this study. Focusing on concrete Banach spaces, we show that even though there are no general variational principles in such spaces for the projection onto subspaces, specific elements satisfy a variational characterization. We provide concrete examples to illustrate various notions of projections in general Banach spaces. Generalized projection Generalized metric projection Generalized proximal set Generalized Chebyshev set Generalized identical points Orthogonal subspaces Li, Jinlu verfasserin aut Enthalten in Journal of mathematical analysis and applications Amsterdam [u.a.] : Elsevier, 1960 531 Online-Ressource (DE-627)266886922 (DE-600)1468566-8 (DE-576)103373101 1096-0813 nnns volume:531 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines VZ AR 531
allfields_unstemmed	10.1016/j.jmaa.2023.127865 doi (DE-627)ELV065689089 (ELSEVIER)S0022-247X(23)00868-5 DE-627 ger DE-627 rda eng 510 VZ 31.00 bkl Khan, Akhtar A. verfasserin aut Characterizations of the metric and generalized metric projections on subspaces of Banach spaces 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The variational principles of the metric projection onto closed and convex sets are commonly used as the basis for characterizations of metric projections onto subspaces of Hilbert spaces. However, it is important to realize that the variational principles do not hold as necessary and sufficient conditions in general Banach spaces to characterize the metric projection and its related extensions. This technical handicap prevents the study of metric projection onto subspaces of general Banach spaces from being fully explored. Motivated by this existing lacuna in the literature, we investigate the metric projection and the generalized metric projection onto subspaces of general Banach spaces in this study. Focusing on concrete Banach spaces, we show that even though there are no general variational principles in such spaces for the projection onto subspaces, specific elements satisfy a variational characterization. We provide concrete examples to illustrate various notions of projections in general Banach spaces. Generalized projection Generalized metric projection Generalized proximal set Generalized Chebyshev set Generalized identical points Orthogonal subspaces Li, Jinlu verfasserin aut Enthalten in Journal of mathematical analysis and applications Amsterdam [u.a.] : Elsevier, 1960 531 Online-Ressource (DE-627)266886922 (DE-600)1468566-8 (DE-576)103373101 1096-0813 nnns volume:531 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines VZ AR 531
allfieldsGer	10.1016/j.jmaa.2023.127865 doi (DE-627)ELV065689089 (ELSEVIER)S0022-247X(23)00868-5 DE-627 ger DE-627 rda eng 510 VZ 31.00 bkl Khan, Akhtar A. verfasserin aut Characterizations of the metric and generalized metric projections on subspaces of Banach spaces 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The variational principles of the metric projection onto closed and convex sets are commonly used as the basis for characterizations of metric projections onto subspaces of Hilbert spaces. However, it is important to realize that the variational principles do not hold as necessary and sufficient conditions in general Banach spaces to characterize the metric projection and its related extensions. This technical handicap prevents the study of metric projection onto subspaces of general Banach spaces from being fully explored. Motivated by this existing lacuna in the literature, we investigate the metric projection and the generalized metric projection onto subspaces of general Banach spaces in this study. Focusing on concrete Banach spaces, we show that even though there are no general variational principles in such spaces for the projection onto subspaces, specific elements satisfy a variational characterization. We provide concrete examples to illustrate various notions of projections in general Banach spaces. Generalized projection Generalized metric projection Generalized proximal set Generalized Chebyshev set Generalized identical points Orthogonal subspaces Li, Jinlu verfasserin aut Enthalten in Journal of mathematical analysis and applications Amsterdam [u.a.] : Elsevier, 1960 531 Online-Ressource (DE-627)266886922 (DE-600)1468566-8 (DE-576)103373101 1096-0813 nnns volume:531 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines VZ AR 531
allfieldsSound	10.1016/j.jmaa.2023.127865 doi (DE-627)ELV065689089 (ELSEVIER)S0022-247X(23)00868-5 DE-627 ger DE-627 rda eng 510 VZ 31.00 bkl Khan, Akhtar A. verfasserin aut Characterizations of the metric and generalized metric projections on subspaces of Banach spaces 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The variational principles of the metric projection onto closed and convex sets are commonly used as the basis for characterizations of metric projections onto subspaces of Hilbert spaces. However, it is important to realize that the variational principles do not hold as necessary and sufficient conditions in general Banach spaces to characterize the metric projection and its related extensions. This technical handicap prevents the study of metric projection onto subspaces of general Banach spaces from being fully explored. Motivated by this existing lacuna in the literature, we investigate the metric projection and the generalized metric projection onto subspaces of general Banach spaces in this study. Focusing on concrete Banach spaces, we show that even though there are no general variational principles in such spaces for the projection onto subspaces, specific elements satisfy a variational characterization. We provide concrete examples to illustrate various notions of projections in general Banach spaces. Generalized projection Generalized metric projection Generalized proximal set Generalized Chebyshev set Generalized identical points Orthogonal subspaces Li, Jinlu verfasserin aut Enthalten in Journal of mathematical analysis and applications Amsterdam [u.a.] : Elsevier, 1960 531 Online-Ressource (DE-627)266886922 (DE-600)1468566-8 (DE-576)103373101 1096-0813 nnns volume:531 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines VZ AR 531
language	English
source	Enthalten in Journal of mathematical analysis and applications 531 volume:531
sourceStr	Enthalten in Journal of mathematical analysis and applications 531 volume:531
format_phy_str_mv	Article
bklname	Mathematik: Allgemeines
institution	findex.gbv.de
topic_facet	Generalized projection Generalized metric projection Generalized proximal set Generalized Chebyshev set Generalized identical points Orthogonal subspaces
dewey-raw	510
isfreeaccess_bool	false
container_title	Journal of mathematical analysis and applications
authorswithroles_txt_mv	Khan, Akhtar A. @@aut@@ Li, Jinlu @@aut@@
publishDateDaySort_date	2023-01-01T00:00:00Z
hierarchy_top_id	266886922
dewey-sort	3510
id	ELV065689089
language_de	englisch
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author	Khan, Akhtar A.
spellingShingle	Khan, Akhtar A. ddc 510 bkl 31.00 misc Generalized projection misc Generalized metric projection misc Generalized proximal set misc Generalized Chebyshev set misc Generalized identical points misc Orthogonal subspaces Characterizations of the metric and generalized metric projections on subspaces of Banach spaces
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topic_title	510 VZ 31.00 bkl Characterizations of the metric and generalized metric projections on subspaces of Banach spaces Generalized projection Generalized metric projection Generalized proximal set Generalized Chebyshev set Generalized identical points Orthogonal subspaces
topic	ddc 510 bkl 31.00 misc Generalized projection misc Generalized metric projection misc Generalized proximal set misc Generalized Chebyshev set misc Generalized identical points misc Orthogonal subspaces
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title	Characterizations of the metric and generalized metric projections on subspaces of Banach spaces
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title_full	Characterizations of the metric and generalized metric projections on subspaces of Banach spaces
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title_sort	characterizations of the metric and generalized metric projections on subspaces of banach spaces
title_auth	Characterizations of the metric and generalized metric projections on subspaces of Banach spaces
abstract	The variational principles of the metric projection onto closed and convex sets are commonly used as the basis for characterizations of metric projections onto subspaces of Hilbert spaces. However, it is important to realize that the variational principles do not hold as necessary and sufficient conditions in general Banach spaces to characterize the metric projection and its related extensions. This technical handicap prevents the study of metric projection onto subspaces of general Banach spaces from being fully explored. Motivated by this existing lacuna in the literature, we investigate the metric projection and the generalized metric projection onto subspaces of general Banach spaces in this study. Focusing on concrete Banach spaces, we show that even though there are no general variational principles in such spaces for the projection onto subspaces, specific elements satisfy a variational characterization. We provide concrete examples to illustrate various notions of projections in general Banach spaces.
abstractGer	The variational principles of the metric projection onto closed and convex sets are commonly used as the basis for characterizations of metric projections onto subspaces of Hilbert spaces. However, it is important to realize that the variational principles do not hold as necessary and sufficient conditions in general Banach spaces to characterize the metric projection and its related extensions. This technical handicap prevents the study of metric projection onto subspaces of general Banach spaces from being fully explored. Motivated by this existing lacuna in the literature, we investigate the metric projection and the generalized metric projection onto subspaces of general Banach spaces in this study. Focusing on concrete Banach spaces, we show that even though there are no general variational principles in such spaces for the projection onto subspaces, specific elements satisfy a variational characterization. We provide concrete examples to illustrate various notions of projections in general Banach spaces.
abstract_unstemmed	The variational principles of the metric projection onto closed and convex sets are commonly used as the basis for characterizations of metric projections onto subspaces of Hilbert spaces. However, it is important to realize that the variational principles do not hold as necessary and sufficient conditions in general Banach spaces to characterize the metric projection and its related extensions. This technical handicap prevents the study of metric projection onto subspaces of general Banach spaces from being fully explored. Motivated by this existing lacuna in the literature, we investigate the metric projection and the generalized metric projection onto subspaces of general Banach spaces in this study. Focusing on concrete Banach spaces, we show that even though there are no general variational principles in such spaces for the projection onto subspaces, specific elements satisfy a variational characterization. We provide concrete examples to illustrate various notions of projections in general Banach spaces.
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title_short	Characterizations of the metric and generalized metric projections on subspaces of Banach spaces
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doi_str	10.1016/j.jmaa.2023.127865
up_date	2024-07-06T23:54:18.017Z
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Characterizations of the metric and generalized metric projections on subspaces of Banach spaces

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