2005/09/07 by T. Bhattacharyya, Bhattacharyya, T., J. Eschmeier +3
Mathematics · #47A13 #47A20 #47A56 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:47A13 #msc:47A20 #msc:47A56
paper · pdf · doi:10.48550/arxiv.math/0509162
18 pages, revised version, to appear in Proc. Math. Sci., Indian Acad. Sci
arxiv created 2006/04/12 · arxiv updated 2009/12/01
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 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.