J. Aust. Math. Soc.
74 (2003), 185199

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

Jun Kawabe
Department of Mathematics
Faculty of Engineering
Shinshu University
4171 Wakasato
Nagano 3808553
Japan
jkawabe@gipwc.shinshuu.ac.jp



Abstract

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.

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