Year: 2023
Author: Chao Zu, Yixin Yang, Yufeng Lu
Communications in Mathematical Research , Vol. 39 (2023), Iss. 3 : pp. 331–341
Abstract
A closed subspace $M$ of the Hardy space $H^2(\mathbb{D}^2)$ over the bidisk is called submodule if it is invariant under multiplication by coordinate functions $z$ and $w.$ Whether every finitely generated submodule is Hilbert-Schmidt is an unsolved problem. This paper proves that every finitely generated submodule $M$ containing $θ(z)−\varphi(w)$ is Hilbert-Schmidt, where $θ(z),$ $\varphi(w)$ are two finite Blaschke products.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2022-0034
Communications in Mathematical Research , Vol. 39 (2023), Iss. 3 : pp. 331–341
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Hardy space over the bidisk Hilbert-Schmidt submodule fringe operator Fredholm index.