On iterated similarities of operators
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- by Domingo A. Herrero PDF
- Proc. Amer. Math. Soc. 72 (1978), 519-520 Request permission
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 $\{ X \in \mathcal {L}(\mathcal {H}):\left \|{A^k}X{A^{ - k}}\right \| \leqslant C(X) < \infty ,k = 0,1,2, \ldots \}$ coincides with $\mathcal {L}(\mathcal {H})$, then A is a multiple of a similarity of a unitary operator.References
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J. A. Deddens, Another characterization of nest algebras (preprint).
- Shôichirô Sakai, $C^*$-algebras and $W^*$-algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60, Springer-Verlag, New York-Heidelberg, 1971. MR 0442701
- Béla de Sz. Nagy, On uniformly bounded linear transformations in Hilbert space, Acta Univ. Szeged. Sect. Sci. Math. 11 (1947), 152–157. MR 22309
Additional Information
- © Copyright 1978 American Mathematical Society
- 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