The () Property in Banach Spaces | Zendy

Danyal Soybaş | Zendy

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The () Property in Banach Spaces

Author(s) -

Danyal Soybaş

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/754531

Subject(s) - mathematics , banach space , approximation property , property (philosophy) , pure mathematics , dual (grammatical number) , infinite dimensional vector function , dual space , banach manifold , space (punctuation) , lp space , computer science , art , philosophy , literature , epistemology , operating system

A Banach space is said to have (D) property if every bounded linear operator ∶→∗ is weakly compact for every Banach space whose dual does not contain an isomorphic copy of ∞. 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 1() of real functions, which are integrable with respect to a measure with values in a Banach space , has (D) property. We give some other results concerning Banach spaces with (D) property

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