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Best approximation of a normal operator in the Schatten $ p$-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 $ \mathfrak{N}(\Lambda )$ denote the normal operators with spectrum contained in $ \Lambda $. Provided there is some N in $ \mathfrak{N}(\Lambda )$ such that $ A - N$ belongs to the Schatten class $ {c_p},p \geqslant 2$, the main result of this paper obtains a best approximation for A from $ \mathfrak{N}(\Lambda )$ 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

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