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Proceedings of the American Mathematical Society

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On iterated similarities of operators


Author: Domingo A. Herrero
Journal: Proc. Amer. Math. Soc. 72 (1978), 519-520
MSC: Primary 47A65
DOI: https://doi.org/10.1090/S0002-9939-1978-0509246-3
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?)

  • [1] J. A. Deddens, Another characterization of nest algebras (preprint).
  • [2] Shôichirô Sakai, 𝐶*-algebras and 𝑊*-algebras, Springer-Verlag, New York-Heidelberg, 1971. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60. MR 0442701
  • [3] Béla de Sz. Nagy, On uniformly bounded linear transformations in Hilbert space, Acta Univ. Szeged. Sect. Sci. Math. 11 (1947), 152–157. MR 0022309

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DOI: https://doi.org/10.1090/S0002-9939-1978-0509246-3
Article copyright: © Copyright 1978 American Mathematical Society

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