On CNC commuting contractive tuples

Bhattacharyya, T. ; Eschmeier, J. ; Sarkar, J. (2006) On CNC commuting contractive tuples Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 116 (3). pp. 299-316. ISSN 0370-0089

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Official URL: http://www.ias.ac.in/describe/article/pmsc/116/03/...

Related URL: http://dx.doi.org/10.1007/BF02829747


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.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Characteristic Function; Invariant Subspaces; Biholomorphic Automorphisms; Functional Model; Coincidence
ID Code:99773
Deposited On:27 Nov 2016 12:52
Last Modified:29 Nov 2016 09:05

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