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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On iterated similarities of operators

Author: Domingo A. Herrero
Journal: Proc. Amer. Math. Soc. 72 (1978), 519-520
MSC: Primary 47A65
MathSciNet review: 509246
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Abstract: Let $ \mathcal{L}(\mathcal{H})$ be the algebra of operators on a complex Hilbert space $ \mathcal{H}$. If $ A \in \mathcal{L}(\mathcal{H})$ is invertible and $ \{ X \in \mathcal{L}(\mathcal{H}):\left\Vert{A^k}X{A^{ - k}}\right\Vert \leqslant C(X) < \infty ,k = 0,1,2, \ldots \} $ coincides with $ \mathcal{L}(\mathcal{H})$, then A is a multiple of a similarity of a unitary operator.

References [Enhancements On Off] (What's this?)

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  • [3] B. Sz.-Nagy, On uniformly bounded linear transformations in Hilbert space, Acta Sci. Math. (Szeged) 11 (1947), 152-157. MR 0022309 (9:191b)

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