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# The Uncomplemented Spaces $W(X,Y)$ and $K(X,Y)$

Published:2009-12-04
Printed: Mar 2010
• Paul Lewis
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## Abstract

Classical results of Kalton and techniques of Feder are used to study the complementation of the space $W(X, Y)$ of weakly compact operators and the space $K(X,Y)$ of compact operators in the space $L(X,Y)$ of all bounded linear maps from X to Y.
 Keywords: spaces of operators, complemented subspace, weakly compact operator, basic sequence
 MSC Classifications: 46B28 - Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20] 46B15 - Summability and bases [See also 46A35] 46B20 - Geometry and structure of normed linear spaces

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