Isometries of certain operator algebras
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- by Brian J. Cole and John Wermer PDF
- Proc. Amer. Math. Soc. 124 (1996), 3047-3053 Request permission
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
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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
- Received by editor(s): January 20, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3047-3053
- MSC (1991): Primary 47D25
- DOI: https://doi.org/10.1090/S0002-9939-96-03482-X
- MathSciNet review: 1343686