Best approximation of a normal operator in the Schatten -norm

Author:
Richard Bouldin

Journal:
Proc. Amer. Math. Soc. **80** (1980), 277-282

MSC:
Primary 47B20

DOI:
https://doi.org/10.1090/S0002-9939-1980-0577759-3

MathSciNet review:
577759

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Abstract: Let *A* be a fixed normal operator and let denote the normal operators with spectrum contained in . Provided there is some *N* in such that belongs to the Schatten class , the main result of this paper obtains a best approximation for *A* from with respect to the Schatten *p*-norm. A necessary and sufficient condition is given for *A* to have a unique best approximation in that case.

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DOI:
https://doi.org/10.1090/S0002-9939-1980-0577759-3

Article copyright:
© Copyright 1980
American Mathematical Society