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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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On injective or dense-range operators leaving a given chain of subspaces invariant
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by Bamdad R. Yahaghi PDF
Proc. Amer. Math. Soc. 132 (2004), 1059-1066 Request permission

Abstract:

In this paper we prove the existence of dense-range or one-to-one compact operators on a separable Banach space leaving a given finite chain of subspaces invariant. We use this result to prove that a semigroup $\mathcal {S}$ of bounded operators is reducible if and only if there exists an appropriate one-to-one compact operator $K$ such that the collection $\mathcal {S} K$ of compact operators is reducible.
References
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Additional Information
  • Bamdad R. Yahaghi
  • Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
  • Email: bamdad5@math.toronto.edu, reza5@mscs.dal.ca
  • Received by editor(s): October 15, 2002
  • Received by editor(s) in revised form: November 16, 2002
  • Published electronically: July 14, 2003
  • Additional Notes: The author gratefully acknowledges the support of an Izaak Walton Killam Memorial Scholarship at Dalhousie University as well as an NSERC PDF at the University of Toronto.

  • Dedicated: With gratitude, dedicated to H. Hajiabolhassan, I. Mirfazeli, and F. Nouri
  • Communicated by: Joseph A. Ball
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1059-1066
  • MSC (2000): Primary 47A15, 47A46, 47D03
  • DOI: https://doi.org/10.1090/S0002-9939-03-07139-9
  • MathSciNet review: 2045421