On CNC Commuting Contractive Tuples

Proceedings Mathematical Sciences

J Sarkar¹  T Bhattacharyya³  J Eschmeier² 

[1] $$;Fachbereich Mathematik, Universität des Saarlandes, Saarbrücken, Germany$$;Department of Mathematics, Indian Institute of Science, Bangalore 0 0, India$$

关键词: Characteristic function;    invariant subspaces;    biholomorphic automorphisms;    functional model;    coincidence.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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 $mathcal{H}$. 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.

【 授权许可】

Unknown