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Joint continuity of injective tensor products of vector measures in Banach lattices

Part of: Classical measure theory Set functions, measures and integrals with values in abstract spaces Topological linear spaces and related structures

Published online by Cambridge University Press:  09 April 2009

Jun Kawabe
Jun Kawabe
Affiliation:
Department of Mathematics Faculty of Engineering Shinshu University4-17-1 Wakasato Nagano 380-8553Japan e-mail: jkawabe@gipwc.shinshu-u.ac.jp
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Abstract

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It is shown that the injective tensor product of positive vector measures in certain Banach lattices is jointly continuous with respect to the weak convergence of vector measures. This result is obtained by a diagonal convergence theorem for injective tensor integrals. Our approach to this problem is based on Bartle's bilinear integration theory.

Keywords

positive vector measureinjective tensor product of vector measuresweak convergence of vector measuresBanach latticeinjective tensor integral.

MSC classification

Secondary: 28A33: Spaces of measures, convergence of measures 28B05: Vector-valued set functions, measures and integrals 46A11: Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) 46A32: Spaces of linear operators; topological tensor products; approximation properties
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 2 , April 2003 , pp. 185 - 200
Copyright
Copyright © Australian Mathematical Society 2003

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