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