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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 \[ \dim N\left ( P \right ) \geq \max \left \{ {\dim N\left ( {{\lambda _i} - A} \right ):1 \leq i \leq n} \right \}.\] It is shown that there exist such projections where we have equality in this inequality.


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Keywords: Compressions, closed linear operators
Article copyright: © Copyright 1992 American Mathematical Society