Annals of Functional Analysis

A note on relative compactness in ${K(X,Y)}$

Ioana Ghenciu

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For Banach spaces $X$ and $Y$, let $K(X,Y)$ denote the space of all compact operators from $X$ to $Y$ endowed with the operator norm. We give sufficient conditions for subsets of $K(X,Y)$ to be relatively compact. We also give some necessary and sufficient conditions for the Dunford–Pettis relatively compact property of some spaces of operators.

Article information

Ann. Funct. Anal. Volume 7, Number 3 (2016), 470-483.

Received: 2 October 2015
Accepted: 26 January 2016
First available in Project Euclid: 19 July 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 46B25: Classical Banach spaces in the general theory 46B28: Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]

compact operators Dunford–Pettis relative compact property Gelfand–Phillips property


Ghenciu, Ioana. A note on relative compactness in K ( X , Y ) . Ann. Funct. Anal. 7 (2016), no. 3, 470--483. doi:10.1215/20088752-3624814.

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