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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A generalization of Lomonosov’s inequality and its applications to invariant subspaces
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by Shamim I. Ansari PDF
Proc. Amer. Math. Soc. 130 (2002), 2905-2909 Request permission

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
  • Received by editor(s): December 15, 2000
  • Published electronically: May 8, 2002
  • Communicated by: David R. Larson
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 2905-2909
  • MSC (2000): Primary 47A15
  • DOI: https://doi.org/10.1090/S0002-9939-02-06644-3
  • MathSciNet review: 1908913