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Uniform property (K) and its related properties

Published online by Cambridge University Press:  17 April 2009

Hong-Kun Xu  and
Giuseppe Marino
Hong-Kun Xu
Affiliation:
Department of MathematicsUniversity of Durban-WestvilleDurban 4000South Africa e-mail: hkxu@pixie.udw.ac.za
Giuseppe Marino
Affiliation:
Dipartimento di MatematicaUniversitá della CalabriaCosenzaItaly e-mail: gmarino@ccuws4.unical.it
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Abstract

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A Banach space X is said to have uniform property (K) if there exists a constant (k ∈ [0,1) such that whenever xn ⇀ 0, ∥xn∥ → 1, and we have lim sup ∥ym∥ ≤ k. This property is the uniform version of property (K) recently introduced by B. Sims (Bull. Austral. Math. Soc. 50(1994), 523–528). Sufficient conditions for uniform property (K) are given. Some examples are presented to separate various Banach space properties. Applications to nonlinear operators are also included.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 1 , February 1998 , pp. 93 - 107
Copyright
Copyright © Australian Mathematical Society 1998

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