On c.n.c. commuting contractive tuples

T. Bhattacharyya; J. Eschmeier; J. Sarkar

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On c.n.c. commuting contractive tuples

T. Bhattacharyya·J. Eschmeier·J. Sarkar

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Abstract

The characteristic function has been an important tool for studying completely non unitary contractions on Hilbert spaces. In this note, we consider completely non-coisometric contractive tuples of commuting operators on a Hilbert space $\clh$. We show that the characteristic function, which is now an operator valued analytic function on the open Euclidean unit ball in $\mathbb{C}^n$, is a complete unitary invariant for such a tuple. We prove that the characteristic function satisfies a natural transformation law under biholomorphic mappings of the unit ball. We also characterize all operator-valued analytic functions which arise as characteristic functions of pure commuting contractive tuples.

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BibTeX RIS

T. Bhattacharyya, J. Eschmeier, J. Sarkar. 2006-04-12. On c.n.c. commuting contractive tuples. https://arxiv.org/abs/math/0509162

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