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Commutators of Operators on Hilbert Space

Published online by Cambridge University Press:  20 November 2018

Arlen Brown ,
P. R. Halmos  and
Carl Pearcy
Arlen Brown
Affiliation:
University of Michigan
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The purpose of this paper is to record some progress on the problem of determining which (bounded, linear) operators A on a separable Hilbert space H are commutators, in the sense that there exist bounded operators B and C on H satisfying A = BC — CB. It is thus natural to consider this paper as a continuation of the sequence (2; 3; 5). In §2 we show that many infinite diagonal matrices (with scalar entries) are commutators and that every weighted unilateral and bilateral shift is a commutator.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 695 - 708
Copyright
Copyright © Canadian Mathematical Society 1965

References

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