Displaying similar documents to “A simple proof of the Borel extension theorem and weak compactness of operators”

A Borel extension approach to weakly compact operators on C 0 ( T )

Thiruvaiyaru V. Panchapagesan (2002)

Czechoslovak Mathematical Journal

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Let X be a quasicomplete locally convex Hausdorff space. Let T be a locally compact Hausdorff space and let C 0 ( T ) = { f T → I , f is continuous and vanishes at infinity } be endowed with the supremum norm. Starting with the Borel extension theorem for X -valued σ -additive Baire measures on T , an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map u C 0 ( T ) → X to be weakly compact.

Lattice-valued Borel measures. III.

Surjit Singh Khurana (2008)

Archivum Mathematicum

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Let X be a completely regular T 1 space, E a boundedly complete vector lattice, C ( X ) ( C b ( X ) ) the space of all (all, bounded), real-valued continuous functions on X . In order convergence, we consider E -valued, order-bounded, σ -additive, τ -additive, and tight measures on X and prove some order-theoretic and topological properties of these measures. Also for an order-bounded, E -valued (for some special E ) linear map on C ( X ) , a measure representation result is proved. In case E n * separates...