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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
Zbl 0912.46011
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