Displaying similar documents to “Completely continuous multilinear operators on C(K)-spaces.”

A Riesz representation theory for completely regular Hausdorff spaces and its applications

Marian Nowak (2016)

Open Mathematics

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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 develop the Riemman-Stieltjes-type Integral representation theory of (β, || · ||F) -continuous operators T : Cb(X, E) → F with respect to the representing Borel operator measures. For X being a k-space, we characterize strongly bounded (β, || · ||F)-continuous operators T : Cb(X, E) → F. As an application,...

Representation of multilinear operators on C(K, X) spaces.

Ignacio Villanueva (2002)

RACSAM

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We present a Riesz type representation theorem for multilinear operators defined on the product of C(K,X) spaces with values in a Banach space. In order to do this we make a brief exposition of the theory of operator valued polymeasures.