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Sufficient conditions for a continuous linear operator to be weakly compact

Published online by Cambridge University Press:  17 April 2009

Joe Howard  and
Kenneth Melendez
Joe Howard
Affiliation:
Department of Mathematics and Statistics, Oklahoma State University, Stillwater, Oklahoma, USA.
Kenneth Melendez
Affiliation:
Department of Mathematics and Statistics, Oklahoma State University, Stillwater, Oklahoma, USA.
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Abstract

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A locally convex topological vector (LCTV) space E is said to have property V (Dieudonné property) if for every complete separated LCTV space F, every unconditionally converging (weakly completely continuous) operator T: E → F is wsakly compact. First, an investigation of the permanence of property V is given. The permanence of the Dieudonné is analogous. Relationships between property V and the Dieudonné property are then given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 2 , October 1972 , pp. 183 - 190
Copyright
Copyright © Australian Mathematical Society 1972

References

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