On the class of order L-weakly and order M-weakly compact operators
Abstract In this paper, we introduce and study new concepts of order L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms. It is proved that if $$T:E \lon...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Lhaimer, Driss [verfasserIn] |
|---|
| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
L-weakly compact operator M-weakly compact operator Order L-weakly compact operator |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Positivity - Springer International Publishing, 1997, 25(2021), 4 vom: 19. Apr., Seite 1569-1578 |
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| Übergeordnetes Werk: |
volume:25 ; year:2021 ; number:4 ; day:19 ; month:04 ; pages:1569-1578 |
| Links: |
|---|
| DOI / URN: |
10.1007/s11117-021-00829-2 |
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OLC2127279360 |
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| 520 | |a Abstract In this paper, we introduce and study new concepts of order L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms. It is proved that if $$T:E \longrightarrow F$$ is an operator between two Banach lattices, then T is order M-weakly compact if and only if its adjoint $$T'$$ is order L-weakly compact. Also, we show that if its adjoint $$T'$$ is order M-weakly compact, then T is order L-weakly compact. Some related results are also obtained. | ||
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10.1007/s11117-021-00829-2 doi (DE-627)OLC2127279360 (DE-He213)s11117-021-00829-2-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Lhaimer, Driss verfasserin aut On the class of order L-weakly and order M-weakly compact operators 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract In this paper, we introduce and study new concepts of order L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms. It is proved that if $$T:E \longrightarrow F$$ is an operator between two Banach lattices, then T is order M-weakly compact if and only if its adjoint $$T'$$ is order L-weakly compact. Also, we show that if its adjoint $$T'$$ is order M-weakly compact, then T is order L-weakly compact. Some related results are also obtained. L-weakly compact operator M-weakly compact operator Order weakly compact operator Order L-weakly compact operator Order M-weakly compact operator Order continuous norm Banach lattice Bouras, Khalid aut Moussa, Mohammed aut Enthalten in Positivity Springer International Publishing, 1997 25(2021), 4 vom: 19. Apr., Seite 1569-1578 (DE-627)243279434 (DE-600)1426263-0 (DE-576)066430526 1385-1292 nnns volume:25 year:2021 number:4 day:19 month:04 pages:1569-1578 https://doi.org/10.1007/s11117-021-00829-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 AR 25 2021 4 19 04 1569-1578 |
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10.1007/s11117-021-00829-2 doi (DE-627)OLC2127279360 (DE-He213)s11117-021-00829-2-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Lhaimer, Driss verfasserin aut On the class of order L-weakly and order M-weakly compact operators 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract In this paper, we introduce and study new concepts of order L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms. It is proved that if $$T:E \longrightarrow F$$ is an operator between two Banach lattices, then T is order M-weakly compact if and only if its adjoint $$T'$$ is order L-weakly compact. Also, we show that if its adjoint $$T'$$ is order M-weakly compact, then T is order L-weakly compact. Some related results are also obtained. L-weakly compact operator M-weakly compact operator Order weakly compact operator Order L-weakly compact operator Order M-weakly compact operator Order continuous norm Banach lattice Bouras, Khalid aut Moussa, Mohammed aut Enthalten in Positivity Springer International Publishing, 1997 25(2021), 4 vom: 19. Apr., Seite 1569-1578 (DE-627)243279434 (DE-600)1426263-0 (DE-576)066430526 1385-1292 nnns volume:25 year:2021 number:4 day:19 month:04 pages:1569-1578 https://doi.org/10.1007/s11117-021-00829-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 AR 25 2021 4 19 04 1569-1578 |
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10.1007/s11117-021-00829-2 doi (DE-627)OLC2127279360 (DE-He213)s11117-021-00829-2-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Lhaimer, Driss verfasserin aut On the class of order L-weakly and order M-weakly compact operators 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract In this paper, we introduce and study new concepts of order L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms. It is proved that if $$T:E \longrightarrow F$$ is an operator between two Banach lattices, then T is order M-weakly compact if and only if its adjoint $$T'$$ is order L-weakly compact. Also, we show that if its adjoint $$T'$$ is order M-weakly compact, then T is order L-weakly compact. Some related results are also obtained. L-weakly compact operator M-weakly compact operator Order weakly compact operator Order L-weakly compact operator Order M-weakly compact operator Order continuous norm Banach lattice Bouras, Khalid aut Moussa, Mohammed aut Enthalten in Positivity Springer International Publishing, 1997 25(2021), 4 vom: 19. Apr., Seite 1569-1578 (DE-627)243279434 (DE-600)1426263-0 (DE-576)066430526 1385-1292 nnns volume:25 year:2021 number:4 day:19 month:04 pages:1569-1578 https://doi.org/10.1007/s11117-021-00829-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 AR 25 2021 4 19 04 1569-1578 |
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10.1007/s11117-021-00829-2 doi (DE-627)OLC2127279360 (DE-He213)s11117-021-00829-2-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Lhaimer, Driss verfasserin aut On the class of order L-weakly and order M-weakly compact operators 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract In this paper, we introduce and study new concepts of order L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms. It is proved that if $$T:E \longrightarrow F$$ is an operator between two Banach lattices, then T is order M-weakly compact if and only if its adjoint $$T'$$ is order L-weakly compact. Also, we show that if its adjoint $$T'$$ is order M-weakly compact, then T is order L-weakly compact. Some related results are also obtained. L-weakly compact operator M-weakly compact operator Order weakly compact operator Order L-weakly compact operator Order M-weakly compact operator Order continuous norm Banach lattice Bouras, Khalid aut Moussa, Mohammed aut Enthalten in Positivity Springer International Publishing, 1997 25(2021), 4 vom: 19. Apr., Seite 1569-1578 (DE-627)243279434 (DE-600)1426263-0 (DE-576)066430526 1385-1292 nnns volume:25 year:2021 number:4 day:19 month:04 pages:1569-1578 https://doi.org/10.1007/s11117-021-00829-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 AR 25 2021 4 19 04 1569-1578 |
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10.1007/s11117-021-00829-2 doi (DE-627)OLC2127279360 (DE-He213)s11117-021-00829-2-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Lhaimer, Driss verfasserin aut On the class of order L-weakly and order M-weakly compact operators 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract In this paper, we introduce and study new concepts of order L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms. It is proved that if $$T:E \longrightarrow F$$ is an operator between two Banach lattices, then T is order M-weakly compact if and only if its adjoint $$T'$$ is order L-weakly compact. Also, we show that if its adjoint $$T'$$ is order M-weakly compact, then T is order L-weakly compact. Some related results are also obtained. L-weakly compact operator M-weakly compact operator Order weakly compact operator Order L-weakly compact operator Order M-weakly compact operator Order continuous norm Banach lattice Bouras, Khalid aut Moussa, Mohammed aut Enthalten in Positivity Springer International Publishing, 1997 25(2021), 4 vom: 19. Apr., Seite 1569-1578 (DE-627)243279434 (DE-600)1426263-0 (DE-576)066430526 1385-1292 nnns volume:25 year:2021 number:4 day:19 month:04 pages:1569-1578 https://doi.org/10.1007/s11117-021-00829-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 AR 25 2021 4 19 04 1569-1578 |
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Abstract In this paper, we introduce and study new concepts of order L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms. It is proved that if $$T:E \longrightarrow F$$ is an operator between two Banach lattices, then T is order M-weakly compact if and only if its adjoint $$T'$$ is order L-weakly compact. Also, we show that if its adjoint $$T'$$ is order M-weakly compact, then T is order L-weakly compact. Some related results are also obtained. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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Abstract In this paper, we introduce and study new concepts of order L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms. It is proved that if $$T:E \longrightarrow F$$ is an operator between two Banach lattices, then T is order M-weakly compact if and only if its adjoint $$T'$$ is order L-weakly compact. Also, we show that if its adjoint $$T'$$ is order M-weakly compact, then T is order L-weakly compact. Some related results are also obtained. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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Abstract In this paper, we introduce and study new concepts of order L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms. It is proved that if $$T:E \longrightarrow F$$ is an operator between two Banach lattices, then T is order M-weakly compact if and only if its adjoint $$T'$$ is order L-weakly compact. Also, we show that if its adjoint $$T'$$ is order M-weakly compact, then T is order L-weakly compact. Some related results are also obtained. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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| up_date |
2024-07-04T10:15:33.636Z |
| _version_ |
1803643134816550913 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2127279360</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230505125408.0</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/s11117-021-00829-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2127279360</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s11117-021-00829-2-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">Lhaimer, Driss</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On the class of order L-weakly and order M-weakly compact operators</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 In this paper, we introduce and study new concepts of order L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms. It is proved that if $$T:E \longrightarrow F$$ is an operator between two Banach lattices, then T is order M-weakly compact if and only if its adjoint $$T'$$ is order L-weakly compact. Also, we show that if its adjoint $$T'$$ is order M-weakly compact, then T is order L-weakly compact. 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7.40199 |