The strong Dunford-Pettis relatively compact property of order p
We introduce and study Banach lattices with the strong Dunford-Pettis relatively compact property of order p (1 ? p < ?); that is, spaces in which every weakly p-compact and almost Dunford-Pettis set is relatively compact. We also introduce the notion of the weak Dunford-Pettis property of order...
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| Veröffentlicht in: | Filomat 2023, Vol.37 (22), p.7339-7349 |
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| container_end_page | 7349 |
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| container_issue | 22 |
| container_start_page | 7339 |
| container_title | Filomat |
| container_volume | 37 |
| creator | Ardakani, Halimeh Taghavinejad, Khadijeh Rezagholi, Sharifeh |
| description | We introduce and study Banach lattices with the strong Dunford-Pettis
relatively compact property of order p (1 ? p < ?); that is, spaces in which
every weakly p-compact and almost Dunford-Pettis set is relatively compact.
We also introduce the notion of the weak Dunford-Pettis property of order p
and then characterize this property in terms of sequences. In particular, in
terms of disjoint weakly compact operators into c0, an operator
characterization of those Banach lattices with the weak Dunford-Pettis
property of order p is given. Moreover, some results about Banach lattices
with the positive Dunford-Pettis relatively compact property of order p are
presented |
| doi_str_mv | 10.2298/FIL2322339A |
| format | Article |
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relatively compact property of order p (1 ? p < ?); that is, spaces in which
every weakly p-compact and almost Dunford-Pettis set is relatively compact.
We also introduce the notion of the weak Dunford-Pettis property of order p
and then characterize this property in terms of sequences. In particular, in
terms of disjoint weakly compact operators into c0, an operator
characterization of those Banach lattices with the weak Dunford-Pettis
property of order p is given. Moreover, some results about Banach lattices
with the positive Dunford-Pettis relatively compact property of order p are
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relatively compact property of order p (1 ? p < ?); that is, spaces in which
every weakly p-compact and almost Dunford-Pettis set is relatively compact.
We also introduce the notion of the weak Dunford-Pettis property of order p
and then characterize this property in terms of sequences. In particular, in
terms of disjoint weakly compact operators into c0, an operator
characterization of those Banach lattices with the weak Dunford-Pettis
property of order p is given. Moreover, some results about Banach lattices
with the positive Dunford-Pettis relatively compact property of order p are
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relatively compact property of order p (1 ? p < ?); that is, spaces in which
every weakly p-compact and almost Dunford-Pettis set is relatively compact.
We also introduce the notion of the weak Dunford-Pettis property of order p
and then characterize this property in terms of sequences. In particular, in
terms of disjoint weakly compact operators into c0, an operator
characterization of those Banach lattices with the weak Dunford-Pettis
property of order p is given. Moreover, some results about Banach lattices
with the positive Dunford-Pettis relatively compact property of order p are
presented</abstract><doi>10.2298/FIL2322339A</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Filomat, 2023, Vol.37 (22), p.7339-7349 |
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| language | eng |
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| source | Jstor Complete Legacy; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| title | The strong Dunford-Pettis relatively compact property of order p |
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