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

Fong, C.; Sourour, A.

doi:10.1090/S0002-9939-03-06910-7

The semigroup generated by a similarity orbit or a unitary orbit of an operator
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by C. K. Fong and A. R. Sourour PDF

Proc. Amer. Math. Soc. 131 (2003), 3203-3210 Request permission

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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