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

DOI:
https://doi.org/10.1090/S0002-9939-03-06910-7

Published electronically:
May 9, 2003

MathSciNet review:
1992861

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let 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 is the group of all invertible operators. If, in addition, is a unitary operator, then the multiplicative semigroup generated by the unitary orbit of 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

Email:
sourour@math.uvic.ca

DOI:
https://doi.org/10.1090/S0002-9939-03-06910-7

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