Extremal compressions of closed operators
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- by K.-H. Förster and K. Jahn
- Proc. Amer. Math. Soc. 114 (1992), 171-174
- DOI: https://doi.org/10.1090/S0002-9939-1992-1068121-6
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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.References
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Bibliographic 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