On a new geometric property for Banach spaces

Rao, T. S. S. R. K. (1997) On a new geometric property for Banach spaces Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 107 (1). pp. 35-42. ISSN 0253-4142

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Official URL: http://www.ias.ac.in/j_archive/mathsci/107/1/35-42...

Related URL: http://dx.doi.org/10.1007/BF02840472

Abstract

In this paper we study a geometric property for Banach spaces called condition (∗), introduced by de Reynaet al in [3]. A Banach space has this property if for any weakly null sequence {xn} of unit vectors in X, if {xn} is any sequence of unit vectors in X that attain their norm at xn's, then xn → 0. We show that a Banach space satisfies condition (∗ ) for all equivalent norms iff the space has the Schur property. We also study two related geometric conditions, one of which is useful in calculating the essential norm of an operator.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Banach Spaces; Schur Property
ID Code:64702
Deposited On:14 Oct 2011 06:43
Last Modified:18 May 2016 13:02

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