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Let X be a completely regular Hausdorff space, and E and F be Banach spaces. Let Crc(X,E) be a space of all continuous functions f:X→E such that f(X) is a relatively compact set in E, equipped with the strict topology βσ. We study (βσ,‖⋅‖F)-continuous strongly bounded operators T:Crc(X,E)→F. In particular, we establish the relationships between (βσ,‖⋅‖F)-continuous strongly bounded operators and weakly...
Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let Cb(X,E) be the space of all E-valued bounded continuous functions on X, equipped with the strict topology β. We study weakly completely continuous and completely continuous operators T:Cb(X,E)→F. We establish the relationship between these classes of operators and the corresponding Borel operator measures given by the Riesz...
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