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# The Uncomplemented Subspace $\mathbf K(X,Y)$

Published:2011-07-04
Printed: Mar 2013
• Ioana Ghenciu,
University of Wisconsin - River Falls, Department of Mathematics, River Falls, WI 54022-5001
 Format: LaTeX MathJax PDF

## Abstract

A vector measure result is used to study the complementation of the space $K(X,Y)$ of compact operators in the spaces $W(X,Y)$ of weakly compact operators, $CC(X,Y)$ of completely continuous operators, and $U(X,Y)$ of unconditionally converging operators. Results of Kalton and Emmanuele concerning the complementation of $K(X,Y)$ in $L(X,Y)$ and in $W(X,Y)$ are generalized. The containment of $c_0$ and $\ell_\infty$ in spaces of operators is also studied.
 Keywords: compact operators, weakly compact operators, uncomplemented subspaces of operators
 MSC Classifications: 46B20 - Geometry and structure of normed linear spaces 46B28 - Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]

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