Beurling quotient modules on the polydisc

Authors

Monojit Bhattacharjee, Indian Institute of Technology Bombay
B. Krishna Das, Indian Institute of Technology Bombay
Ramlal Debnath, Indian Statistical Institute Bangalore
Jaydeb Sarkar, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Journal of Functional Analysis

Abstract

Let H2(Dn) denote the Hardy space over the polydisc Dn, n≥2. A closed subspace Q⊆H2(Dn) is called Beurling quotient module if there exists an inner function θ∈H∞(Dn) such that Q=H2(Dn)/θH2(Dn). We present a complete characterization of Beurling quotient modules of H2(Dn): Let Q⊆H2(Dn) be a closed subspace, and let Czi=PQMzi|Q, i=1,…,n. Then Q is a Beurling quotient module if and only if (IQ−Czi⁎Czi)(IQ−Czj⁎Czj)=0(i≠j). We present two applications: first, we obtain a dilation theorem for Brehmer n-tuples of commuting contractions, and, second, we relate joint invariant subspaces with factorizations of inner functions. All results work equally well for general vector-valued Hardy spaces.

DOI

10.1016/j.jfa.2021.109258

Publication Date

1-1-2022

Comments

Open Access, Green

Recommended Citation

Bhattacharjee, Monojit; Krishna Das, B.; Debnath, Ramlal; and Sarkar, Jaydeb, "Beurling quotient modules on the polydisc" (2022). Journal Articles. 3412.
https://digitalcommons.isical.ac.in/journal-articles/3412