A Beurling Theorem For Generalized Hardy Spaces On A Multiply Connected Domain
Keywords
AõLiated operator; Beurling theorem; Forelli projection; Gauge norm; Generalized Hardy space; Inner-outer factorization; Invariant subspace; Multiply connected domain
Abstract
The object of this paper is to prove a version of the Beurling-Helson-Lowdenslager invariant subspace theorem for operators on certain Banach spaces of functions on a multiply connected domain in C. The norms for these spaces are either the usual Lebesgue and Hardy space norms or certain continuous gauge norms. In the Hardy space case the expected corollaries include the characterization of the cyclic vectors as the outer functions in this context, a demonstration that the set of analytic multiplication operators is maximal abelian and reflexive, and a determination of the closed operators that commute with all analytic multiplication operators.
Publication Date
6-1-2018
Publication Title
Canadian Journal of Mathematics
Volume
70
Issue
3
Number of Pages
515-537
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.4153/CJM-2017-007-8
Copyright Status
Unknown
Socpus ID
85048804555 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/85048804555
STARS Citation
Chen, Yanni; Hadwin, Don; Liu, Zhe; and Nordgren, Eric, "A Beurling Theorem For Generalized Hardy Spaces On A Multiply Connected Domain" (2018). Scopus Export 2015-2019. 9862.
https://stars.library.ucf.edu/scopus2015/9862