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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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Spectrally determined growth is generic
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by Michael Renardy
Proc. Amer. Math. Soc. 124 (1996), 2451-2453
DOI: https://doi.org/10.1090/S0002-9939-96-03417-X

Abstract:

Let $A$ be the infinitesimal generator of a $C_0$-semigroup of operators in a Hilbert space. We consider the class of operators $A+B$, where $B$ is bounded. It is proved that the spectrum of $A+B$ determines the growth of the associated semigroup for “most" operators $B$ (in the sense of Baire category).
References
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Bibliographic Information
  • Michael Renardy
  • Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123
  • Email: renardym@math.vt.edu
  • Received by editor(s): January 9, 1995
  • Received by editor(s) in revised form: February 23, 1995
  • Additional Notes: This research was supported by the National Science Foundation under Grant DMS–9306635 and by the Office of Naval Research under Grant N00014–92–J–1664.
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 2451-2453
  • MSC (1991): Primary 47D06
  • DOI: https://doi.org/10.1090/S0002-9939-96-03417-X
  • MathSciNet review: 1328372