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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An elementary proof of the characterization of isomorphisms of standard operator algebras
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by Mohammad B. Asadi and A. Khosravi PDF
Proc. Amer. Math. Soc. 134 (2006), 3255-3256 Request permission

Abstract:

This study provides an elementary proof of the well-known fact that any isomorphism $\pi : \mathcal {A}\to \mathcal {B}$ of standard operator algebras on normed spaces $X , Y$, respectively, is spatial; i.e., there exists a topological isomorphism $T : X \to Y$ such that $\pi (A) = TAT^{-1}$ for any $A \in \mathcal {A}$. In particular, $\pi$ is continuous.
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Additional Information
  • Mohammad B. Asadi
  • Affiliation: Faculty of Mathematical Sciences and Computer Engineering, Teacher Training University, 599 Taleghani Avenue, Tehran 15614, Iran
  • Email: mb.asadi@gmail.com
  • A. Khosravi
  • Affiliation: Faculty of Mathematical Sciences and Computer Engineering, Teacher Training University, 599 Taleghani Avenue, Tehran 15614, Iran
  • Email: khosravi@saba.tmu.ac.ir
  • Received by editor(s): May 13, 2005
  • Received by editor(s) in revised form: May 18, 2005
  • Published electronically: May 8, 2006
  • Communicated by: Joseph A. Ball
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 3255-3256
  • MSC (2000): Primary 47B49
  • DOI: https://doi.org/10.1090/S0002-9939-06-08375-4
  • MathSciNet review: 2231909