1. The (D) Property in Banach Spaces.
- Author
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Soybaş, Danyal
- Subjects
- *
BANACH spaces , *LINEAR operators , *ISOMORPHISM (Mathematics) , *INTEGRABLE functions , *GEOMETRIC analysis - Abstract
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 Pelczyn´ski (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. [ABSTRACT FROM AUTHOR]
- Published
- 2012
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