On quotient modules of H²(Dⁿ): essential normality and boundary representations

Authors

B. Krishna Das, Indian Institute of Technology Bombay
Sushil Gorai, Indian Institute of Science Education and Research Kolkata
Jaydeb Sarkar, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Proceedings of the Royal Society of Edinburgh Section A: Mathematics

Abstract

Let Dn be the open unit polydisc in Cn n ≥ 1, and let H2(Dn) be the Hardy space over Dn. For n≥ 3, we show that if θ ϵ H∞(n) is an inner function, then the n-tuple of commuting operators on the Beurling type quotient module Qθ is not essentially normal, where Qθ = H2(Dn)/θH2(Dn) and Czj = PQθMzj|Qθ (j = 1, ⋯ n). Rudin's quotient modules of H2(2) are also shown to be not essentially normal. We prove several results concerning boundary representations of C∗-algebras corresponding to different classes of quotient modules including doubly commuting quotient modules and homogeneous quotient modules.

First Page

1339

Last Page

1359

DOI

10.1017/prm.2018.124

Publication Date

6-1-2020

Recommended Citation

Das, B. Krishna; Gorai, Sushil; and Sarkar, Jaydeb, "On quotient modules of H²(Dⁿ): essential normality and boundary representations" (2020). Journal Articles. 293.
https://digitalcommons.isical.ac.in/journal-articles/293