Which operators are the self-commutators of compact operators?

Authors:
Peng Fan and Che Kao Fong

Journal:
Proc. Amer. Math. Soc. **80** (1980), 58-60

MSC:
Primary 47B05; Secondary 47B47

DOI:
https://doi.org/10.1090/S0002-9939-1980-0574508-X

MathSciNet review:
574508

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that, for a hermitian operator *T* on a Hubert space *H*, the following three statements are equivalent: (i) for some compact operator *A*, (ii) there is an orthonormal basis such that for all *j*, and (iii) (possibly infinite) where and .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1980-0574508-X

Keywords:
Self-commutator,
compact operator,
trace

Article copyright:
© Copyright 1980
American Mathematical Society