The (𝐷) Property in Banach Spaces
A Banach space 𝐸 is said to have (D) property if every bounded linear operator 𝑇∶𝐹→𝐸∗ is weakly compact for every Banach space 𝐹 whose dual does not contain an isomorphic copy of 𝑙∞. Studying this property in connection with other geometric properties, we show that every Banach space whose dual has...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/754531 |
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| author | Danyal Soybaş |
| author_facet | Danyal Soybaş |
| author_sort | Danyal Soybaş |
| collection | DOAJ |
| description | A Banach space 𝐸 is said to have (D) property if every bounded linear operator 𝑇∶𝐹→𝐸∗ is weakly compact for every Banach space 𝐹 whose dual does not contain an isomorphic copy of 𝑙∞. Studying this property in connection with other geometric properties, we show that every Banach space whose dual has (V∗) property of Pełczyński (and hence every Banach space with (V) property) has (D) property. We show that the space 𝐿1(𝑣) of real functions, which are integrable with respect to a measure 𝑣 with values in a Banach space 𝑋, has (D) property. We give some other results concerning Banach spaces with (D) property. |
| format | Article |
| id | doaj-art-0db2f0fa374846158c41b269d55b5e0f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0db2f0fa374846158c41b269d55b5e0f2025-02-03T05:58:41ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/754531754531The (𝐷) Property in Banach SpacesDanyal Soybaş0Mathematics Education Department, Erciyes University, 38039 Kayseri, TurkeyA Banach space 𝐸 is said to have (D) property if every bounded linear operator 𝑇∶𝐹→𝐸∗ is weakly compact for every Banach space 𝐹 whose dual does not contain an isomorphic copy of 𝑙∞. Studying this property in connection with other geometric properties, we show that every Banach space whose dual has (V∗) property of Pełczyński (and hence every Banach space with (V) property) has (D) property. We show that the space 𝐿1(𝑣) of real functions, which are integrable with respect to a measure 𝑣 with values in a Banach space 𝑋, has (D) property. We give some other results concerning Banach spaces with (D) property.http://dx.doi.org/10.1155/2012/754531 |
| spellingShingle | Danyal Soybaş The (𝐷) Property in Banach Spaces Abstract and Applied Analysis |
| title | The (𝐷) Property in Banach Spaces |
| title_full | The (𝐷) Property in Banach Spaces |
| title_fullStr | The (𝐷) Property in Banach Spaces |
| title_full_unstemmed | The (𝐷) Property in Banach Spaces |
| title_short | The (𝐷) Property in Banach Spaces |
| title_sort | 𝐷 property in banach spaces |
| url | http://dx.doi.org/10.1155/2012/754531 |
| work_keys_str_mv | AT danyalsoybas thedpropertyinbanachspaces AT danyalsoybas dpropertyinbanachspaces |