A canonical trace class approximant

Authors:
D. A. Legg and J. D. Ward

Journal:
Proc. Amer. Math. Soc. **93** (1985), 653-656

MSC:
Primary 47B10; Secondary 47A30

DOI:
https://doi.org/10.1090/S0002-9939-1985-0776197-2

MathSciNet review:
776197

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Abstract: Let be a finite-dimensional Hilbert space, the space of bounded linear operators on , and a convex subset of . If is a fixed operator in , then has a unique best approximant from in the norm for . However, in the (trace) norm, may have many best approximants from . In this paper, it is shown that the best approximants to converge to a select trace class approximant as . Furthermore, is the unique trace class approximant minimizing over all trace class approximants . The numbers are the eigenvalues of the positive part of .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1985-0776197-2

Article copyright:
© Copyright 1985
American Mathematical Society