Hilbert-Schmidtness of Submodules in $H^2 (\mathbb{D}^2 )$ Containing $θ(z)−\varphi (w)$

DOI10.4208/cmr.2022-0034OpenAlexW4366129006MaRDI QIDQ6122954

Chao Zu, Yixin Yang, Yu Feng Lu

Publication date: 4 March 2024

Published in: Communications in Mathematical Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/cmr.2022-0034

zbMATH Keywords

fringe operatorHardy space over the bidiskFredholm indexHilbert-Schmidt submodule

Mathematics Subject Classification ID

Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65)

Cites Work

• \(N_\phi\)-type quotient modules on the torus
• Beurling type theorem on the Bergman space via the Hardy space of the bidisk
• Hilbert-schmidtness of some finitely generated submodules in \(H^2(\mathbb{D}^2)\)
• Beurling's phenomenon in two variables
• The core operator and the compressed multipliers on \(M_{\psi,\varphi}\)-type submodules
• The core operator and congruent submodules
• Wold-type decompositions and wandering subspaces for operators close to isometries
• Multiplication operators on the Bergman space via the Hardy space of the bidisk
• The core function of submodules over the bidisk
• A brief survey on operator theory in $H^2(\mathbb D^2)$
• Operator theory in the Hardy space over the bidisk. III
• Operator theory in the Hardy space over the bidisk. II
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