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Smoothness in $${\mathcal L}{(C(X),C(Y))}$$. (English) Zbl 0883.46016
Summary: Let $${\mathbf B}({\mathcal L}(C(X),C(Y)))$$ be the unit ball of the space of operators acting from the space of continuous functions $$C(X)$$ into $$C(Y)$$ ($$X$$, $$Y$$ – compact metric spaces). The purpose of this paper is to give a characterization of the smooth points of $${\mathbf B}({\mathcal L}(C(X),C(Y)))$$.
##### MSC:
 46B28 Spaces of operators; tensor products; approximation properties 46B20 Geometry and structure of normed linear spaces
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