The Uncomplemented Subspace $\mathbf K(X,Y) $
Printed: Mar 2013
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.
compact operators, weakly compact operators, uncomplemented subspaces of operators
46B20 - Geometry and structure of normed linear spaces
46B28 - Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]