## On the uncomplemented subspace $$K(X,Y)$$.(English)Zbl 0776.46016

Let $$X$$ and $$Y$$ be Banach spaces.It is a long-standing conjecture that either every operator from $$X$$ to $$Y$$ is compact or the subspace of compact operators is uncomplemented. It is proved in this paper that the above conjecture holds if $$K(X,Y)$$ contains a copy of $$c_ 0$$. [The same result has been obtained by G. Emmanuele, Math. Proc. Cambridge Philos. Soc. 111, 331-335 (1992)].
Reviewer: D.Werner (Berlin)

### MSC:

 46B28 Spaces of operators; tensor products; approximation properties 47L05 Linear spaces of operators

### Keywords:

uncomplemented subspace; spaces of compact operators
Full Text:

### References:

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