A Note on Sequential Properties of Noncompactness in Banach Spaces |
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Authors: | E A Sánchez Pérez |
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Institution: | (1) E.T.S.I. Caminos Canales y Puertos, Camino de Vera, 46072 Valencia, Spain E-mail |
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Abstract: | We define two properties of sequences in Banach spaces that may be related to measures of noncompactness of subsets of these
spaces. The first one concerns properties of sequences related to the strong topology, and the second one is related to the
weak topology. Given a Banach space X, we introduce a new Banach space such that we can find a subset E in it that may be identified with the balls in the first one. We use compactness in this new space to characterize our sequential
properties. In particular, we prove a general form of the Eberlein-Smulian theorem.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | |
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