Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Isometries of certain operator algebras


Authors: Brian J. Cole and John Wermer
Journal: Proc. Amer. Math. Soc. 124 (1996), 3047-3053
MSC (1991): Primary 47D25.
MathSciNet review: 1343686
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: To a given basis $\phi _1,\dotsc ,\phi _n$ on an $n$-dimensional Hilbert space $\mathcal H$, we associate the algebra $\mathfrak A$ of all linear operators on $\mathcal H$ having every $\phi _j$ as an eigenvector. So, $\mathfrak A$ is commutative, semisimple, and $n$-dimensional. Given two algebras of this type, $\mathfrak A$ and $\mathfrak B$, there is a natural algebraic isomorphism $\tau $ of $\mathfrak A$ and $\mathfrak B$. We study the question: When does $\tau $ preserve the operator norm?


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47D25.

Retrieve articles in all journals with MSC (1991): 47D25.


Additional Information

Brian J. Cole
Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912
Email: Brian_Cole@brown.edu

John Wermer
Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912
Email: John_Wermer@brown.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03482-X
PII: S 0002-9939(96)03482-X
Received by editor(s): January 20, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society