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The semigroup generated by a similarity orbit or a unitary orbit of an operator

Authors: C. K. Fong and A. R. Sourour
Journal: Proc. Amer. Math. Soc. 131 (2003), 3203-3210
MSC (2000): Primary 47D03; Secondary 20F38
Published electronically: May 9, 2003
MathSciNet review: 1992861
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Abstract: Let $T$ be an invertible operator that is not a scalar modulo the ideal of compact operators. We show that the multiplicative semigroup generated by the similarity orbit of $T$ is the group of all invertible operators. If, in addition, $T$ is a unitary operator, then the multiplicative semigroup generated by the unitary orbit of $T$ is the group of all unitary operators.

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Additional Information

C. K. Fong
Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6

A. R. Sourour
Affiliation: Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada V8W 3P4

Keywords: Semigroups, conjugation-invariant
Received by editor(s): November 22, 2000
Received by editor(s) in revised form: May 17, 2002
Published electronically: May 9, 2003
Additional Notes: This research was supported in part by an NSERC grant.
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society

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