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Projections from \(L(X,Y)\) onto \(K(X,Y)\). (English) Zbl 1050.46016
The author proves, under some assumptions on the spaces \(X\) and \(Y\), a lower estimate of the norm of a projection from the space of linear operators from \(X\) to \(Y\) onto the subspace formed by compact operators. This extends and simplifies results of P. D. Saphar [Proc. Am. Math. Soc. 127, 1127–1131 (1999; Zbl 0912.46011)]. The results are somehow related to the long-standing problem whether \(K(X,Y)=L(X,Y)\) whenever \(K(X,Y)\) is complemented in \(L(X,Y)\).
MSC:
46B28 Spaces of operators; tensor products; approximation properties
Citations:
Zbl 0912.46011
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