## Kamil John

*Projections from $L(X,Y)$ onto $K(X,Y)$ *

Comment.Math.Univ.Carolinae 41,4 (2000) 765-771. **Abstract:**Generalization of certain results in [Sap] and simplification of the proofs are given. We observe e.g.: Let $X$ and $Y$ be Banach spaces such that $X$ is weakly compactly generated Asplund space and $X^*$ has the approximation property (respectively $Y$ is weakly compactly generated Asplund space and $Y^*$ has the approximation property). Suppose that $L(X,Y)\not =K(X,Y)$ and let $1<\lambda <2$. Then $X$ (respectively $Y$) can be equivalently renormed so that any projection $P$ of $L(X,Y)$ onto $K(X,Y)$ has the sup-norm greater or equal to $\lambda $.

**Keywords:** compact operator, approximation property, reflexive Banach space, projection, separability

**AMS Subject Classification:** 46B28

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