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Weak convergence of tensor products of vector measures with values in nuclear spaces

Published online by Cambridge University Press:  17 April 2009

Jun Kawabe
Jun Kawabe
Affiliation:
Department of Mathematics, Faculty of EngineeringShinshu University500 Wakasato Nagano 380-8553, Japan e-mail: jkawabe@gipwc.shinshu-u.ac.jp
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Abstract

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We study weak convergence of tensor products of vector measures with values in nuclear spaces, such as the space of all rapidly decreasing, infinitely differentiable functions, the space of all test functions, and the strong duals of those spaces. It is shown that the weak convergence of a net of tensor products of vector measures follows from that of the corresponding net of real product measures.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 3 , June 1999 , pp. 449 - 458
Copyright
Copyright © Australian Mathematical Society 1999

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