Local Approximate Symmetry of Birkhoff–James Orthogonality in Normed Linear Spaces
Abstract Two different notions of approximate Birkhoff–James orthogonality in normed linear spaces have been introduced by Dragomir and Chmieliński. In the present paper we consider a global and a local approximate symmetry of the Birkhoff–James orthogonality related to each of the two definitions....
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Chmieliński, Jacek [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Results in mathematics - Springer International Publishing, 1984, 76(2021), 3 vom: 17. Juni |
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| Übergeordnetes Werk: |
volume:76 ; year:2021 ; number:3 ; day:17 ; month:06 |
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| DOI / URN: |
10.1007/s00025-021-01437-y |
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| 520 | |a Abstract Two different notions of approximate Birkhoff–James orthogonality in normed linear spaces have been introduced by Dragomir and Chmieliński. In the present paper we consider a global and a local approximate symmetry of the Birkhoff–James orthogonality related to each of the two definitions. We prove that the considered orthogonality is approximately symmetric in the sense of Dragomir in all finite-dimensional Banach spaces. For the other case, we prove that for finite-dimensional polyhedral Banach spaces, the approximate symmetry of the orthogonality is equivalent to some newly introduced geometric property. Our investigations complement and extend the scope of some recent results on a global approximate symmetry of the Birkhoff–James orthogonality. | ||
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10.1007/s00025-021-01437-y doi (DE-627)OLC2126121836 (DE-He213)s00025-021-01437-y-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Chmieliński, Jacek verfasserin aut Local Approximate Symmetry of Birkhoff–James Orthogonality in Normed Linear Spaces 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract Two different notions of approximate Birkhoff–James orthogonality in normed linear spaces have been introduced by Dragomir and Chmieliński. In the present paper we consider a global and a local approximate symmetry of the Birkhoff–James orthogonality related to each of the two definitions. We prove that the considered orthogonality is approximately symmetric in the sense of Dragomir in all finite-dimensional Banach spaces. For the other case, we prove that for finite-dimensional polyhedral Banach spaces, the approximate symmetry of the orthogonality is equivalent to some newly introduced geometric property. Our investigations complement and extend the scope of some recent results on a global approximate symmetry of the Birkhoff–James orthogonality. Birkhoff–James orthogonality approximate Birkhoff–James orthogonality C-approximate symmetry D-approximate symmetry Khurana, Divya aut Sain, Debmalya aut Enthalten in Results in mathematics Springer International Publishing, 1984 76(2021), 3 vom: 17. Juni (DE-627)129571423 (DE-600)226632-5 (DE-576)015060160 1422-6383 nnns volume:76 year:2021 number:3 day:17 month:06 https://doi.org/10.1007/s00025-021-01437-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4277 AR 76 2021 3 17 06 |
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10.1007/s00025-021-01437-y doi (DE-627)OLC2126121836 (DE-He213)s00025-021-01437-y-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Chmieliński, Jacek verfasserin aut Local Approximate Symmetry of Birkhoff–James Orthogonality in Normed Linear Spaces 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract Two different notions of approximate Birkhoff–James orthogonality in normed linear spaces have been introduced by Dragomir and Chmieliński. In the present paper we consider a global and a local approximate symmetry of the Birkhoff–James orthogonality related to each of the two definitions. We prove that the considered orthogonality is approximately symmetric in the sense of Dragomir in all finite-dimensional Banach spaces. For the other case, we prove that for finite-dimensional polyhedral Banach spaces, the approximate symmetry of the orthogonality is equivalent to some newly introduced geometric property. Our investigations complement and extend the scope of some recent results on a global approximate symmetry of the Birkhoff–James orthogonality. Birkhoff–James orthogonality approximate Birkhoff–James orthogonality C-approximate symmetry D-approximate symmetry Khurana, Divya aut Sain, Debmalya aut Enthalten in Results in mathematics Springer International Publishing, 1984 76(2021), 3 vom: 17. Juni (DE-627)129571423 (DE-600)226632-5 (DE-576)015060160 1422-6383 nnns volume:76 year:2021 number:3 day:17 month:06 https://doi.org/10.1007/s00025-021-01437-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4277 AR 76 2021 3 17 06 |
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Abstract Two different notions of approximate Birkhoff–James orthogonality in normed linear spaces have been introduced by Dragomir and Chmieliński. In the present paper we consider a global and a local approximate symmetry of the Birkhoff–James orthogonality related to each of the two definitions. We prove that the considered orthogonality is approximately symmetric in the sense of Dragomir in all finite-dimensional Banach spaces. For the other case, we prove that for finite-dimensional polyhedral Banach spaces, the approximate symmetry of the orthogonality is equivalent to some newly introduced geometric property. Our investigations complement and extend the scope of some recent results on a global approximate symmetry of the Birkhoff–James orthogonality. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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Abstract Two different notions of approximate Birkhoff–James orthogonality in normed linear spaces have been introduced by Dragomir and Chmieliński. In the present paper we consider a global and a local approximate symmetry of the Birkhoff–James orthogonality related to each of the two definitions. We prove that the considered orthogonality is approximately symmetric in the sense of Dragomir in all finite-dimensional Banach spaces. For the other case, we prove that for finite-dimensional polyhedral Banach spaces, the approximate symmetry of the orthogonality is equivalent to some newly introduced geometric property. Our investigations complement and extend the scope of some recent results on a global approximate symmetry of the Birkhoff–James orthogonality. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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Abstract Two different notions of approximate Birkhoff–James orthogonality in normed linear spaces have been introduced by Dragomir and Chmieliński. In the present paper we consider a global and a local approximate symmetry of the Birkhoff–James orthogonality related to each of the two definitions. We prove that the considered orthogonality is approximately symmetric in the sense of Dragomir in all finite-dimensional Banach spaces. For the other case, we prove that for finite-dimensional polyhedral Banach spaces, the approximate symmetry of the orthogonality is equivalent to some newly introduced geometric property. Our investigations complement and extend the scope of some recent results on a global approximate symmetry of the Birkhoff–James orthogonality. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2126121836</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230505122419.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230505s2021 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00025-021-01437-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2126121836</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00025-021-01437-y-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Chmieliński, Jacek</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Local Approximate Symmetry of Birkhoff–James Orthogonality in Normed Linear Spaces</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Two different notions of approximate Birkhoff–James orthogonality in normed linear spaces have been introduced by Dragomir and Chmieliński. In the present paper we consider a global and a local approximate symmetry of the Birkhoff–James orthogonality related to each of the two definitions. We prove that the considered orthogonality is approximately symmetric in the sense of Dragomir in all finite-dimensional Banach spaces. For the other case, we prove that for finite-dimensional polyhedral Banach spaces, the approximate symmetry of the orthogonality is equivalent to some newly introduced geometric property. 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