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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A generalization of Lomonosov's inequality and its applications to invariant subspaces


Author: Shamim I. Ansari
Journal: Proc. Amer. Math. Soc. 130 (2002), 2905-2909
MSC (2000): Primary 47A15
Published electronically: May 8, 2002
MathSciNet review: 1908913
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Abstract: In this article we generalize Victor Lomonosov's famous inequality so as to be applicable to a wider class of functions. Then using it we prove that the adjoint of an algebra with a compactness property which is weaker than the PS property, employed by Victor Lomonosov, has nontrivial invariant subspaces.


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Additional Information

Shamim I. Ansari
Affiliation: Department of Mathematics and Statistics, Mississippi State University, P.O. Box MA, Mississippi State, Mississippi 39762
Email: shmansr@aol.com

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06644-3
PII: S 0002-9939(02)06644-3
Received by editor(s): December 15, 2000
Published electronically: May 8, 2002
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society