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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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