Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2013; 50(5): 933-944

Printed September 1, 2013

https://doi.org/10.4134/JKMS.2013.50.5.933

Copyright © The Korean Mathematical Society.

On continuous module homomorphisms between random locally convex modules

Xia Zhang

Tianjin Polytechnic University

Abstract

Based on the four kinds of theoretical definitions of the continuous module homomorphism between random locally convex modules, we first show that among them there are only two essentially. Further, we prove that such two are identical if the family of $L^{0}$-seminorms for the former random locally convex module has the countable concatenation property, meantime we also provide a counterexample which shows that it is necessary to require the countable concatenation property.

Keywords: random locally convex modules, $(\varepsilon,\lambda)$-topology, locally $L^{0}$-convex topology, continuous module homomorphisms

MSC numbers: Primary 46H25, 46A03, 46E10

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