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)

 
 

 

Isomorphisms of standard operator algebras


Author: Peter Šemrl
Journal: Proc. Amer. Math. Soc. 123 (1995), 1851-1855
MSC: Primary 47D30
DOI: https://doi.org/10.1090/S0002-9939-1995-1242104-8
MathSciNet review: 1242104
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let X and Y be Banach spaces, $\dim X = \infty$, and let $\mathcal {A}$ and $\mathcal {B}$ be standard operator algebras on X and Y, respectively. Assume that $\phi :\mathcal {A} \to \mathcal {B}$ is a bijective mapping satisfying $\left \| {\phi (AB) - \phi (A)\phi (B)} \right \| \leq \varepsilon ,A,B \in \mathcal {A}$, where $\varepsilon$ is a given positive real number (no linearity or continuity of $\phi$ is assumed). Then $\phi$ is a spatially implemented linear or conjugate linear algebra isomorphism. In particular, $\phi$ is continuous.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47D30

Retrieve articles in all journals with MSC: 47D30


Additional Information

Article copyright: © Copyright 1995 American Mathematical Society