Commuting row contractions with polynomial characteristic functions

Authors

Monojit Bhattacharjee, Birla Institute of Technology and Science, Pilani
Kalpesh J. Haria, Indian Institute of Technology Goa
Jaydeb Sarkar, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Acta Scientiarum Mathematicarum

Abstract

A characteristic function is a special operator-valued analytic function defined on the open unit ball of Cn associated with an n-tuple of commuting row contraction on some Hilbert space. In this paper, we continue our study of the representations of n-tuples of commuting row contractions on Hilbert spaces, which have polynomial characteristic functions. Gleason’s problem plays an important role in the representations of row contractions. We further complement the representations of our row contractions by proving the-orems concerning factorizations of characteristic functions. We also emphasize the importance and the role of noncommutative operator theory and noncom-mutative varieties to the classification problem of polynomial characteristic functions.

First Page

429

Last Page

461

DOI

10.14232/actasm-020-303-x

Publication Date

1-1-2021

Comments

Open Access, Green

Recommended Citation

Bhattacharjee, Monojit; Haria, Kalpesh J.; and Sarkar, Jaydeb, "Commuting row contractions with polynomial characteristic functions" (2021). Journal Articles. 2127.
https://digitalcommons.isical.ac.in/journal-articles/2127