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The semigroup generated by a similarity orbit or a unitary orbit of an operator
Author(s):
C.
K.
Fong;
A.
R.
Sourour
Journal:
Proc. Amer. Math. Soc.
131
(2003),
3203-3210.
MSC (2000):
Primary 47D03;
Secondary 20F38
Posted:
May 9, 2003
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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:
10.1090/S0002-9939-03-06910-7
PII:
S 0002-9939(03)06910-7
Keywords:
Semigroups,
conjugation-invariant
Received by editor(s):
November 22, 2000
Received by editor(s) in revised form:
May 17, 2002
Posted:
May 9, 2003
Additional Notes:
This research was supported in part by an NSERC grant.
Communicated by:
David R. Larson
Copyright of article:
Copyright
2003,
American Mathematical Society
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