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Weak Sequential Completeness of 𝑲(X,Y)

Published online by Cambridge University Press:  20 November 2018

Qingying Bu
Qingying Bu*
Affiliation:
Department of Mathematics, University of Mississippi, University, MS 38677, USA e-mail: [email protected]
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Abstract

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For Banach spaces $X$ and $Y$, we show that if ${{X}^{*}}$ and $Y$ are weakly sequentially complete and every weakly compact operator from $X$ to $Y$ is compact, then the space of all compact operators from $X$ to $Y$ is weakly sequentially complete. The converse is also true if, in addition, either ${{X}^{*}}$ or $Y$ has the bounded compact approximation property.

Keywords

46B2546B28weak sequential completenessreflexivitycompact operator space
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 3 , 01 September 2013 , pp. 503 - 509
Copyright
Copyright © Canadian Mathematical Society 2013

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