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Trace-Class Operators in CSL Algebras

Published online by Cambridge University Press:  20 November 2018

Shlomo Rosenoer
Shlomo Rosenoer*
Affiliation:
Department of Mathematics University of Toronto Toronto, Ontario, Canada M5S 1A1
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Abstract

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In this note we show that if 𝓛 is a commutative subspace lattice, then every trace-class operator in Alg 𝓛 lies in the norm-closure of the span of rank-one operators in Alg 𝓛. We also give an elementary proof of a recent result of Davidson and Pitts that if 𝓛 is a CSL generated by completely distributive lattice and finitely many commuting chains, then 𝓛 is compact in the strong operator topology if and only if 𝓛 is completely distributive.

Keywords

47D2546L10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 3 , 01 September 1992 , pp. 416 - 422
Copyright
Copyright © Canadian Mathematical Society 1992

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