On c.n.c. commuting contractive tuples

Details On c.n.c. commuting contractive tuples On c.n.c. commuting contractive tuples

2005-09-07

arxiv.org/abs/math/0509162v2

Mathematics

Operator Algebras

18 pages, revised version, to appear in Proc. Math. Sci., Indian Acad. Sci

Scientific paper

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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