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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Extremal compressions of closed operators


Authors: K.-H. Förster and K. Jahn
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
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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

$\displaystyle \dim N\left( P \right) \geq \max \left\{ {\dim N\left( {{\lambda _i} - A} \right):1 \leq i \leq n} \right\}.$

It is shown that there exist such projections where we have equality in this inequality.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1068121-6
Keywords: Compressions, closed linear operators
Article copyright: © Copyright 1992 American Mathematical Society