Elementary operators and invariant subalgebras

Author:
Keith J. Coates

Journal:
Proc. Amer. Math. Soc. **124** (1996), 3437-3441

MSC (1991):
Primary 47D25; Secondary 47A15

DOI:
https://doi.org/10.1090/S0002-9939-96-03481-8

MathSciNet review:
1343685

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Abstract | References | Similar Articles | Additional Information

Abstract: We provide an example of an elementary operator which leaves invariant a nest algebra but which cannot be written as a finite sum of multiplications each of which leaves the nest algebra invariant. We also prove that the given operator lies in the completely bounded norm closure of the linear span of the multiplications which leave the nest algebra invariant.

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Additional Information

**Keith J. Coates**

Affiliation:
Department of Mathematics, Illinois Wesleyan University, Bloomington, Illinois 61702

Email:
kcoates@sun.iwu.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03481-8

Received by editor(s):
September 8, 1994

Received by editor(s) in revised form:
May 18, 1995

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1996
American Mathematical Society