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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Invariant subspaces for Banach space operators with an annular spectral set
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by Onur Yavuz PDF
Trans. Amer. Math. Soc. 360 (2008), 2661-2680 Request permission

Abstract:

Consider an annulus $\Omega =\{z\in \mathbb {C}:r_ {0}<|z|<1\}$ for some $0<r_{0}<1$, and let $T$ be a bounded invertible linear operator on a Banach space $X$ whose spectrum contains $\partial \Omega$. Assume there exists a constant $K>0$ such that $\|p(T)\|~\leq ~ K \sup \{|p(\lambda )|:|\lambda |\leq 1\}$ and $\|p(r_0T^{-1})\|\leq K \sup \{|p(\lambda )|:|\lambda |\leq 1\}$ for all polynomials $p$. Then there exists a nontrivial common invariant subspace for $T^{*}$ and ${T^{*}}^{-1}$.
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Additional Information
  • Onur Yavuz
  • Affiliation: Department of Mathematics, Indiana University, Rawles Hall, Bloomington, Indiana 47405
  • Address at time of publication: Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
  • Email: oyavuz@indiana.edu, oyavuz@metu.edu.tr
  • Received by editor(s): May 2, 2005
  • Received by editor(s) in revised form: April 17, 2006
  • Published electronically: December 11, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 2661-2680
  • MSC (2000): Primary 47A15; Secondary 47A60
  • DOI: https://doi.org/10.1090/S0002-9947-07-04324-3
  • MathSciNet review: 2373328