Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A65

Retrieve articles in all journals with MSC: 47A65

Additional Information

Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society