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 |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |