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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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Extremal compressions of closed operators
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by K.-H. Förster and K. Jahn PDF
Proc. Amer. Math. Soc. 114 (1992), 171-174 Request permission

Abstract:

Let $X$ be a Banach space, $A$ a closed linear operator on $X$, and ${\lambda _1}, \ldots ,{\lambda _n}$ isolated eigenvalues of $A$ of finite multiplicity. If $P$ is a projection on $X$ such that ${\lambda _1}, \ldots ,{\lambda _n}$ belong to the resolvent of the compression of $A$ on the range of $P$ it is easy to see that \[ \dim N\left ( P \right ) \geq \max \left \{ {\dim N\left ( {{\lambda _i} - A} \right ):1 \leq i \leq n} \right \}.\] It is shown that there exist such projections where we have equality in this inequality.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 114 (1992), 171-174
  • MSC: Primary 47A10; Secondary 47A20, 47A55
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1068121-6
  • MathSciNet review: 1068121