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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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: 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