On CNC commuting contractive tuples |
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Authors: | T Bhattacharyya J Eschmeier J Sarkar |
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Institution: | 1. Department of Mathematics, Indian Institute of Science, 560 012, Bangalore, India 2. Fachbereich Mathematik, Universit?t des Saarlandes, 66123, Saarbrücken, Germany
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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 H. We show
that the characteristic function, which is now an operator-valued analytic function on the open Euclidean unit ball in ℂn, 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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Keywords: | Characteristic function invariant subspaces biholomorphic automorphisms functional model coincidence |
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