Spectral approximations of a normal operator

Author:
Richard Bouldin

Journal:
Proc. Amer. Math. Soc. **76** (1979), 279-284

MSC:
Primary 47B15

MathSciNet review:
537088

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Abstract: If is a closed convex set in the complex plane then denotes all the normal (bounded linear) operators on the fixed separable Hilbert space *H* with spectrum contained in . The fixed operator *A* has *N* as an -approximant provided *N* belongs to and the operator norm equals , the distance from *A* to . With some hypothesis on , this note proves that the dimension of the convex set of all -approximants of normal operator *A* is where is the orthogonal complement of and is the unique distaince minimizing retract of the complex plane onto .

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DOI:
https://doi.org/10.1090/S0002-9939-1979-0537088-2

Article copyright:
© Copyright 1979
American Mathematical Society