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Convergence tensor products and a strict topology

Published online by Cambridge University Press:  17 April 2009

Bernd Müller
Bernd Müller
Affiliation:
Universität Mannheim, Fakultät für Mathematik und Informatik, D-68 Mannheim, Germany.
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Abstract

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We are interested in the strict topology τ on , the set L(E, F) of all continuous linear mappings from E into a Banach space F endowed with the topology of pointwise convergence. The T3-completion of the convergence tensor product E ⊗cLc F is the set of all τ-continuous linear functionals on L(E, F) and τ is the topology of uniform convergence on the compact subsets of . In the case that E is a nuclear Fréchet space, a nuclear (DF)-space or a Banach space with the bounded approximation property the topology τ agrees with the topology of Lco (E, F).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 21 , Issue 2 , May 1980 , pp. 281 - 301
Copyright
Copyright © Australian Mathematical Society 1980

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