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.References
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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