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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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The spectrum of a selfadjoint compression of a self-adjoint operator.

Author: John M. Hosack
Journal: Proc. Amer. Math. Soc. 25 (1970), 83-85
MSC: Primary 47.30
MathSciNet review: 0271760
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Abstract: The relation between the spectrum of a selfadjoint operator and the spectrum of its compression is investigated. In particular, we show that the compression of a selfadjoint operator is essentially selfadjoint if and only if the spectrum of the closure of the compression is contained in the closed convex hull of the spectrum of the operator. Relations between two conceptions of compressions or projections of operators are also considered.

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Keywords: Compression of operator, projection of operator, selfadjoint operator, normal operator, spectrum of compression, completely reducing subspace
Article copyright: © Copyright 1970 American Mathematical Society