Uniqueness of commuting compact approximations

Authors:
Richard B. Holmes, Bruce E. Scranton and Joseph D. Ward

Journal:
Trans. Amer. Math. Soc. **208** (1975), 330-340

MSC:
Primary 47A65

DOI:
https://doi.org/10.1090/S0002-9947-1975-0380480-0

MathSciNet review:
0380480

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Abstract: Let be an infinite dimensional complex Hilbert space, and let (resp. ) be the algebra of all bounded (resp. compact) linear operators on . It is well known that every has a best approximation from the subspace . The purpose of this paper is to study the uniqueness problem concerning the best approximation of a bounded linear operator by compact operators. Our criterion for selecting a unique representative from the set of best approximants is that the representative should commute with . In particular, many familiar operators are shown to have zero as a unique commuting best approximant.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1975-0380480-0

Article copyright:
© Copyright 1975
American Mathematical Society