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A note on the lattice properties of the linear maps of finite rank

Published online by Cambridge University Press:  17 April 2009

John W. Chaney
John W. Chaney
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Illinois, USA.
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Abstract

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It is shown that if E is a barreled locally convex lattice and F is a quasi-complete and order complete locally convex lattice then E′ ⊗ F equipped with the cone of positive continuous linear maps of finite rank is a lattice if and only if E′ or F has finite dimensional order intervals.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 8 , Issue 3 , June 1973 , pp. 343 - 353
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Peressini, Anthony L., Ordered topological vector spaces (Harper and Row, New York, Evanston, and London, 1967).Google Scholar
[2]Schaefer, Helmut H., Topological vector spaces (The Macmillan Company, New York; Collier-Macmillan, London, 1966).Google Scholar