## Best approximation of a normal operator in the Schatten $p$-norm

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- by Richard Bouldin
- Proc. Amer. Math. Soc.
**80**(1980), 277-282 - DOI: https://doi.org/10.1090/S0002-9939-1980-0577759-3
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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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## Bibliographic Information

- © Copyright 1980 American Mathematical Society
- 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