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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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The structure and asymptotic behavior of polynomially compact operators
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by Frank Gilfeather
Proc. Amer. Math. Soc. 25 (1970), 127-134
DOI: https://doi.org/10.1090/S0002-9939-1970-0257791-3

Abstract:

A. R. Bernstein and A. Robinson proved that every polynomially compact operator in Hilbert space has nontrivial invariant subspaces. This paper gives a structure theorem for these operators. We show that a polynomially compact operator is the finite sum of translates of operators which have the property that a finite power of the operator is compact. Furthermore, the spectrum of polynomially compact operators is completely described. Conditions are given to determine the weak and strong asymptotic behavior of a polynomially compact contraction in Hilbert space.
References
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Bibliographic Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 25 (1970), 127-134
  • MSC: Primary 47.40
  • DOI: https://doi.org/10.1090/S0002-9939-1970-0257791-3
  • MathSciNet review: 0257791