On CNC commuting contractive tuples
T Bhattacharyya J Eschmeier J Sarkar
Click here to view fulltext PDF
Permanent link:
https://www.ias.ac.in/article/fulltext/pmsc/116/03/0299-0316
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.
T Bhattacharyya1 J Eschmeier2 J Sarkar1
Volume 132, 2022
All articles
Continuous Article Publishing mode
Click here for Editorial Note on CAP Mode
© 2022-2023 Indian Academy of Sciences, Bengaluru.