Arkiv för Matematik

  • Ark. Mat.
  • Volume 46, Number 1 (2008), 113-142.

Geometry of spaces of compact operators

Åsvald Lima and Vegard Lima

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We introduce the notion of compactly locally reflexive Banach spaces and show that a Banach space X is compactly locally reflexive if and only if $\mathcal{K}(Y,X^{**})\subseteq\mathcal{K}(Y,X)^{**}$ for all reflexive Banach spaces Y. We show that X* has the approximation property if and only if X has the approximation property and is compactly locally reflexive. The weak metric approximation property was recently introduced by Lima and Oja. We study two natural weak compact versions of this property. If X is compactly locally reflexive then these two properties coincide. We also show how these properties are related to the compact approximation property and the compact approximation property with conjugate operators for dual spaces.

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Ark. Mat., Volume 46, Number 1 (2008), 113-142.

Received: 3 March 2006
First available in Project Euclid: 31 January 2017

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2007 © Institut Mittag-Leffler


Lima, Åsvald; Lima, Vegard. Geometry of spaces of compact operators. Ark. Mat. 46 (2008), no. 1, 113--142. doi:10.1007/s11512-007-0060-y.

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