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Topological decompositions of the duals of locally convex operator spaces

Published online by Cambridge University Press:  24 October 2008

D. J. Fleming  and
D. M. Giarrusso
D. J. Fleming
Affiliation:
St Lawrence University, Canton, New York 13617
D. M. Giarrusso
Affiliation:
St Lawrence University, Canton, New York 13617
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Extract

If Z and E are Hausdorff locally convex spaces (LCS) then by Lb(Z, E) we mean the space of continuous linear maps from Z to E endowed with the topology of uniform convergence on the bounded subsets of Z. The dual Lb(Z, E)′ will always carry the topology of uniform convergence on the bounded subsets of Lb(Z, E). If K(Z, E) is a linear subspace of L(Z, E) then Kb(Z, E) will be used to denote K(Z, E) with the relative topology and Kb(Z, E)″ will mean the dual of Kb(Z, E)′ with the natural topology of uniform convergence on the equicontinuous subsets of Kb(Z, E)′. If Z and E are Banach spaces these provide, in each instance, the usual norm topologies.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 2 , March 1983 , pp. 307 - 314
Copyright
Copyright © Cambridge Philosophical Society 1983

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