Journal of Operator Theory

Volume 34, Issue 2, Fall 1995 pp. 307-314.

Hilbert-Schmidt and finite rank operators in CSL algebras

Authors: M. Anoussis (1) and E.G. Katsoulis (2)
Author institution:(1) Department of Mathematics, University of the Aegean, 83200 Karlovasi, GREECE
(2) Department of Mathematics, East Carolina University, Greenville, NC 27858, U.S.A.

Summary: In this note certain results on the structure of the finite rank subalgebra of a CSL algebra are proved. These enable us to show that there are CSLs not generated by any finite family of CD CSLs.

Keywords: CSL algebra, complete distributivity, Hilbert-Schmidt operator, finite rank operator.

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