Displaying similar documents to “Integral multilinear forms on C ( K , X ) spaces”

A simple proof of the Borel extension theorem and weak compactness of operators

Ivan Dobrakov, Thiruvaiyaru V. Panchapagesan (2002)

Czechoslovak Mathematical Journal

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Let T be a locally compact Hausdorff space and let C 0 ( T ) be the Banach space of all complex valued continuous functions vanishing at infinity in T , provided with the supremum norm. Let X be a quasicomplete locally convex Hausdorff space. A simple proof of the theorem on regular Borel extension of X -valued σ -additive Baire measures on T is given, which is more natural and direct than the existing ones. Using this result the integral representation and weak compactness of a continuous linear...

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.

Order convergence of vector measures on topological spaces

Surjit Singh Khurana (2008)

Mathematica Bohemica

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Let X be a completely regular Hausdorff space, E a boundedly complete vector lattice, C b ( X ) the space of all, bounded, real-valued continuous functions on X , ℱ the algebra generated by the zero-sets of X , and μ C b ( X ) → E a positive linear map. First we give a new proof that μ extends to a unique, finitely additive measure μ ℱ → E + such that ν is inner regular by zero-sets and outer regular by cozero sets. Then some order-convergence theorems about nets of E + -valued finitely additive measures on ℱ are proved,...