The ( ð · ) Property in Banach Spaces

Danyal Soybaş

Abstract and Applied Analysis, 2012, vol. 2012, 1-7

Abstract:

A Banach space ð ¸ is said to have ( D ) property if every bounded linear operator 𠑇 ∶ ð ¹ â†’ ð ¸ âˆ— is weakly compact for every Banach space ð ¹ whose dual does not contain an isomorphic copy of ð ‘™ ∞ . 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 ð ¿ 1 ( ð ‘£ ) of real functions, which are integrable with respect to a measure ð ‘£ with values in a Banach space ð ‘‹ , has ( D ) property. We give some other results concerning Banach spaces with ( D ) property.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:754531

DOI: 10.1155/2012/754531

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