Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Isometries of certain operator algebras

Author(s): Brian J. Cole; John Wermer
Journal: Proc. Amer. Math. Soc. 124 (1996), 3047-3053.
MSC (1991): Primary 47D25.
MathSciNet review: 1343686
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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:

1.: B. Cole, K. Lewis, and J. Wermer, A characterization of Pick bodies, J. London Math. Soc. 48 (1993), 316--328. MR 95a:30032
2.: B. Lotto, Von Neumann's inequality for commuting, diagonalizable contractions, I, Proc. Amer. Math. Soc. 120 (1994), 889--901. MR 94e:47012
3.: D. Sarason, Generalized interpolation in $H^\infty$ , Trans. Amer. Math. Soc. 127 (1967), 179--203. MR 34:8193

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