On b-AM-compact and AM-compact operators
Abstract Recently B. Aqzzouz and J H’Michane introduced the class of b-AM-compact operators and studied some of its properties. In this paper, we give some new characterizations of this class of operators. In this regard, it will be focused on the duality property of b-AM-compact operators. Also, we...
Ausführliche Beschreibung
Autor*in: |
Hajji, Mohamed [verfasserIn] |
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Englisch |
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2022 |
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Anmerkung: |
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 |
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Übergeordnetes Werk: |
Enthalten in: Positivity - Springer International Publishing, 1997, 26(2022), 3 vom: 15. Juni |
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Übergeordnetes Werk: |
volume:26 ; year:2022 ; number:3 ; day:15 ; month:06 |
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DOI / URN: |
10.1007/s11117-022-00922-0 |
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Katalog-ID: |
OLC2078916862 |
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520 | |a Abstract Recently B. Aqzzouz and J H’Michane introduced the class of b-AM-compact operators and studied some of its properties. In this paper, we give some new characterizations of this class of operators. In this regard, it will be focused on the duality property of b-AM-compact operators. Also, we introduce a ‘new’ notion of set in normed Riesz space called $$\Vert $$.$$\Vert -$$b-order bounded set and we prove that any bounded operator T from a normed Riesz space E into a Banach space X such that T carries each $$\Vert $$.$$\Vert -$$b-order bounded set of E into a relatively compact set of X extends to b-AM-compact operator from $$\hat{E}$$ (where $$\hat{E}$$ is the completion of E) into X. Finally, we close this paper by new results concerning the domination problem by AM-compact operators. | ||
650 | 4 | |a AM-compact operator | |
650 | 4 | |a b-AM-compact operator | |
650 | 4 | |a LW-compact operator | |
650 | 4 | |a b-order bounded set | |
650 | 4 | |a L-weakly compact set | |
650 | 4 | |a Relatively compact set | |
650 | 4 | |a Order continuous norm | |
650 | 4 | |a Domination | |
700 | 1 | |a Mahfoudhi, Mounir |0 (orcid)0000-0002-8406-6618 |4 aut | |
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10.1007/s11117-022-00922-0 doi (DE-627)OLC2078916862 (DE-He213)s11117-022-00922-0-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Hajji, Mohamed verfasserin aut On b-AM-compact and AM-compact operators 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 Abstract Recently B. Aqzzouz and J H’Michane introduced the class of b-AM-compact operators and studied some of its properties. In this paper, we give some new characterizations of this class of operators. In this regard, it will be focused on the duality property of b-AM-compact operators. Also, we introduce a ‘new’ notion of set in normed Riesz space called $$\Vert $$.$$\Vert -$$b-order bounded set and we prove that any bounded operator T from a normed Riesz space E into a Banach space X such that T carries each $$\Vert $$.$$\Vert -$$b-order bounded set of E into a relatively compact set of X extends to b-AM-compact operator from $$\hat{E}$$ (where $$\hat{E}$$ is the completion of E) into X. Finally, we close this paper by new results concerning the domination problem by AM-compact operators. AM-compact operator b-AM-compact operator LW-compact operator b-order bounded set L-weakly compact set Relatively compact set Order continuous norm Domination Mahfoudhi, Mounir (orcid)0000-0002-8406-6618 aut Enthalten in Positivity Springer International Publishing, 1997 26(2022), 3 vom: 15. Juni (DE-627)243279434 (DE-600)1426263-0 (DE-576)066430526 1385-1292 nnns volume:26 year:2022 number:3 day:15 month:06 https://doi.org/10.1007/s11117-022-00922-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 AR 26 2022 3 15 06 |
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10.1007/s11117-022-00922-0 doi (DE-627)OLC2078916862 (DE-He213)s11117-022-00922-0-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Hajji, Mohamed verfasserin aut On b-AM-compact and AM-compact operators 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 Abstract Recently B. Aqzzouz and J H’Michane introduced the class of b-AM-compact operators and studied some of its properties. In this paper, we give some new characterizations of this class of operators. In this regard, it will be focused on the duality property of b-AM-compact operators. Also, we introduce a ‘new’ notion of set in normed Riesz space called $$\Vert $$.$$\Vert -$$b-order bounded set and we prove that any bounded operator T from a normed Riesz space E into a Banach space X such that T carries each $$\Vert $$.$$\Vert -$$b-order bounded set of E into a relatively compact set of X extends to b-AM-compact operator from $$\hat{E}$$ (where $$\hat{E}$$ is the completion of E) into X. Finally, we close this paper by new results concerning the domination problem by AM-compact operators. AM-compact operator b-AM-compact operator LW-compact operator b-order bounded set L-weakly compact set Relatively compact set Order continuous norm Domination Mahfoudhi, Mounir (orcid)0000-0002-8406-6618 aut Enthalten in Positivity Springer International Publishing, 1997 26(2022), 3 vom: 15. Juni (DE-627)243279434 (DE-600)1426263-0 (DE-576)066430526 1385-1292 nnns volume:26 year:2022 number:3 day:15 month:06 https://doi.org/10.1007/s11117-022-00922-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 AR 26 2022 3 15 06 |
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10.1007/s11117-022-00922-0 doi (DE-627)OLC2078916862 (DE-He213)s11117-022-00922-0-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Hajji, Mohamed verfasserin aut On b-AM-compact and AM-compact operators 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 Abstract Recently B. Aqzzouz and J H’Michane introduced the class of b-AM-compact operators and studied some of its properties. In this paper, we give some new characterizations of this class of operators. In this regard, it will be focused on the duality property of b-AM-compact operators. Also, we introduce a ‘new’ notion of set in normed Riesz space called $$\Vert $$.$$\Vert -$$b-order bounded set and we prove that any bounded operator T from a normed Riesz space E into a Banach space X such that T carries each $$\Vert $$.$$\Vert -$$b-order bounded set of E into a relatively compact set of X extends to b-AM-compact operator from $$\hat{E}$$ (where $$\hat{E}$$ is the completion of E) into X. Finally, we close this paper by new results concerning the domination problem by AM-compact operators. AM-compact operator b-AM-compact operator LW-compact operator b-order bounded set L-weakly compact set Relatively compact set Order continuous norm Domination Mahfoudhi, Mounir (orcid)0000-0002-8406-6618 aut Enthalten in Positivity Springer International Publishing, 1997 26(2022), 3 vom: 15. Juni (DE-627)243279434 (DE-600)1426263-0 (DE-576)066430526 1385-1292 nnns volume:26 year:2022 number:3 day:15 month:06 https://doi.org/10.1007/s11117-022-00922-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 AR 26 2022 3 15 06 |
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10.1007/s11117-022-00922-0 doi (DE-627)OLC2078916862 (DE-He213)s11117-022-00922-0-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Hajji, Mohamed verfasserin aut On b-AM-compact and AM-compact operators 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 Abstract Recently B. Aqzzouz and J H’Michane introduced the class of b-AM-compact operators and studied some of its properties. In this paper, we give some new characterizations of this class of operators. In this regard, it will be focused on the duality property of b-AM-compact operators. Also, we introduce a ‘new’ notion of set in normed Riesz space called $$\Vert $$.$$\Vert -$$b-order bounded set and we prove that any bounded operator T from a normed Riesz space E into a Banach space X such that T carries each $$\Vert $$.$$\Vert -$$b-order bounded set of E into a relatively compact set of X extends to b-AM-compact operator from $$\hat{E}$$ (where $$\hat{E}$$ is the completion of E) into X. Finally, we close this paper by new results concerning the domination problem by AM-compact operators. AM-compact operator b-AM-compact operator LW-compact operator b-order bounded set L-weakly compact set Relatively compact set Order continuous norm Domination Mahfoudhi, Mounir (orcid)0000-0002-8406-6618 aut Enthalten in Positivity Springer International Publishing, 1997 26(2022), 3 vom: 15. Juni (DE-627)243279434 (DE-600)1426263-0 (DE-576)066430526 1385-1292 nnns volume:26 year:2022 number:3 day:15 month:06 https://doi.org/10.1007/s11117-022-00922-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 AR 26 2022 3 15 06 |
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10.1007/s11117-022-00922-0 doi (DE-627)OLC2078916862 (DE-He213)s11117-022-00922-0-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Hajji, Mohamed verfasserin aut On b-AM-compact and AM-compact operators 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 Abstract Recently B. Aqzzouz and J H’Michane introduced the class of b-AM-compact operators and studied some of its properties. In this paper, we give some new characterizations of this class of operators. In this regard, it will be focused on the duality property of b-AM-compact operators. Also, we introduce a ‘new’ notion of set in normed Riesz space called $$\Vert $$.$$\Vert -$$b-order bounded set and we prove that any bounded operator T from a normed Riesz space E into a Banach space X such that T carries each $$\Vert $$.$$\Vert -$$b-order bounded set of E into a relatively compact set of X extends to b-AM-compact operator from $$\hat{E}$$ (where $$\hat{E}$$ is the completion of E) into X. Finally, we close this paper by new results concerning the domination problem by AM-compact operators. AM-compact operator b-AM-compact operator LW-compact operator b-order bounded set L-weakly compact set Relatively compact set Order continuous norm Domination Mahfoudhi, Mounir (orcid)0000-0002-8406-6618 aut Enthalten in Positivity Springer International Publishing, 1997 26(2022), 3 vom: 15. Juni (DE-627)243279434 (DE-600)1426263-0 (DE-576)066430526 1385-1292 nnns volume:26 year:2022 number:3 day:15 month:06 https://doi.org/10.1007/s11117-022-00922-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 AR 26 2022 3 15 06 |
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Abstract Recently B. Aqzzouz and J H’Michane introduced the class of b-AM-compact operators and studied some of its properties. In this paper, we give some new characterizations of this class of operators. In this regard, it will be focused on the duality property of b-AM-compact operators. Also, we introduce a ‘new’ notion of set in normed Riesz space called $$\Vert $$.$$\Vert -$$b-order bounded set and we prove that any bounded operator T from a normed Riesz space E into a Banach space X such that T carries each $$\Vert $$.$$\Vert -$$b-order bounded set of E into a relatively compact set of X extends to b-AM-compact operator from $$\hat{E}$$ (where $$\hat{E}$$ is the completion of E) into X. Finally, we close this paper by new results concerning the domination problem by AM-compact operators. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 |
abstractGer |
Abstract Recently B. Aqzzouz and J H’Michane introduced the class of b-AM-compact operators and studied some of its properties. In this paper, we give some new characterizations of this class of operators. In this regard, it will be focused on the duality property of b-AM-compact operators. Also, we introduce a ‘new’ notion of set in normed Riesz space called $$\Vert $$.$$\Vert -$$b-order bounded set and we prove that any bounded operator T from a normed Riesz space E into a Banach space X such that T carries each $$\Vert $$.$$\Vert -$$b-order bounded set of E into a relatively compact set of X extends to b-AM-compact operator from $$\hat{E}$$ (where $$\hat{E}$$ is the completion of E) into X. Finally, we close this paper by new results concerning the domination problem by AM-compact operators. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 |
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Abstract Recently B. Aqzzouz and J H’Michane introduced the class of b-AM-compact operators and studied some of its properties. In this paper, we give some new characterizations of this class of operators. In this regard, it will be focused on the duality property of b-AM-compact operators. Also, we introduce a ‘new’ notion of set in normed Riesz space called $$\Vert $$.$$\Vert -$$b-order bounded set and we prove that any bounded operator T from a normed Riesz space E into a Banach space X such that T carries each $$\Vert $$.$$\Vert -$$b-order bounded set of E into a relatively compact set of X extends to b-AM-compact operator from $$\hat{E}$$ (where $$\hat{E}$$ is the completion of E) into X. Finally, we close this paper by new results concerning the domination problem by AM-compact operators. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 |
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On b-AM-compact and AM-compact operators |
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https://doi.org/10.1007/s11117-022-00922-0 |
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Mahfoudhi, Mounir |
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Mahfoudhi, Mounir |
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10.1007/s11117-022-00922-0 |
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2024-07-03T22:43:26.572Z |
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