On the reflexivity of multivariable isometries
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- by Jörg Eschmeier PDF
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Abstract:
Let $A \subset C(K)$ be a unital closed subalgebra of the algebra of all continuous functions on a compact set $K$ in $\mathbb {C}^n$. We define the notion of an $A$–isometry and show that, under a suitable regularity condition needed to apply Aleksandrov’s work on the inner function problem, every $A$–isometry $T \in L(\mathcal H)^n$ is reflexive. This result applies to commuting isometries, spherical isometries, and more generally, to all subnormal tuples with normal spectrum contained in the Bergman-Shilov boundary of a strictly pseudoconvex or bounded symmetric domain.References
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Additional Information
- Jörg Eschmeier
- Affiliation: Fachrichtung Mathematik, Universität des Saarlandes, Postfach 151150, D–66041 Saarbrücken, Germany
- Email: eschmei@math.uni-sb.de
- Received by editor(s): January 14, 2005
- Received by editor(s) in revised form: January 31, 2005
- Published electronically: December 15, 2005
- Communicated by: Joseph A. Ball
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 1783-1789
- MSC (2000): Primary 47A15; Secondary 47A13, 47B20, 47L45
- DOI: https://doi.org/10.1090/S0002-9939-05-08139-6
- MathSciNet review: 2207494