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Proceedings of the American Mathematical Society

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An elementary proof of the characterization of isomorphisms of standard operator algebras


Authors: Mohammad B. Asadi and A. Khosravi
Journal: Proc. Amer. Math. Soc. 134 (2006), 3255-3256
MSC (2000): Primary 47B49
DOI: https://doi.org/10.1090/S0002-9939-06-08375-4
Published electronically: May 8, 2006
MathSciNet review: 2231909
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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

Keywords: Standard operator spaces, dual space, bounded operator
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
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.