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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Restrictions of bounded linear operators: Closed range
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by Bruce A. Barnes PDF
Proc. Amer. Math. Soc. 135 (2007), 1735-1740 Request permission

Abstract:

Let $T$ be a bounded linear operator on a Banach space $X,$ and let $W$ be a subspace of $X$ which is a Banach space and $T-$ invariant. Denote by $T_{W}$ the restriction of $T$ to $W.$ This paper explores the questions: $\circ$ If the range of $T$ is closed, under what conditions is the range of $T_{W}$ closed? $\circ$ If the range of $T_{W}$ is closed, under what conditions is the range of $T$ closed?
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Additional Information
  • Bruce A. Barnes
  • Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
  • Email: barnes@uoregon.edu
  • Received by editor(s): September 9, 2005
  • Received by editor(s) in revised form: December 28, 2005
  • Published electronically: November 15, 2006
  • Communicated by: Joseph A. Ball
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 1735-1740
  • MSC (2000): Primary 47A05
  • DOI: https://doi.org/10.1090/S0002-9939-06-08624-2
  • MathSciNet review: 2286083