Bulletin of the Australian Mathematical Society

Table of Contents - Volume 8 - Issue03

Research Article

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

John W. Chaneya1

a1 Department of Mathematics, University of Illinois at Urbana-Champaign, Illinois, USA.

Abstract

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′ xs2297 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.

(Received December 12 1972)

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]