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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 subspace-hypercyclic operators
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by Can Minh Le PDF
Proc. Amer. Math. Soc. 139 (2011), 2847-2852 Request permission

Abstract:

In this paper we study an operator $T$ on a Banach space $E$ which is $M$-hypercyclic for some subspace $M$ of $E$. We give a sufficient condition for such an operator to be $M$-hypercyclic and use it to answer negatively two questions asked by Madore and Martínez-Avendaño. We also give a sufficient condition for $T$ to be $M$-hypercyclic for all finite co-dimensional subspaces $M$ in $E$.
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Additional Information
  • Can Minh Le
  • Affiliation: Department of Mathematics and Sciences, Kent State University, Kent, Ohio 44242
  • Email: cle@math.kent.edu
  • Received by editor(s): May 4, 2010
  • Received by editor(s) in revised form: July 28, 2010
  • Published electronically: January 7, 2011
  • Additional Notes: The author would like to express his thanks to Professor Richard M. Aron for his invaluable advice.
  • Communicated by: Nigel J. Kalton
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 2847-2852
  • MSC (2010): Primary 47A16; Secondary 47B37, 37B99
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10754-8
  • MathSciNet review: 2801626