The Agler reducing subspace for the operator-valued inner function over the bidisk

DOI10.1007/s00020-022-02696-2zbMath1501.47021OpenAlexW4229064438WikidataQ114232090 ScholiaQ114232090MaRDI QIDQ2140262

Senhua Zhu, Yixin Yang, Yu Feng Lu

Publication date: 20 May 2022

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00020-022-02696-2

zbMATH Keywords

vector-valued Hardy spacecompressed shiftAgler reducing subspace

Mathematics Subject Classification ID

Spaces of vector- and operator-valued functions (46E40) Invariant subspaces of linear operators (47A15) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Linear operators on function spaces (general) (47B38)

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Cites Work

• Properties of Beurling-type submodules via Agler decompositions
• Beurling type quotient modules over the bidisk and boundary representations
• Realization and interpolation for Schur--Agler-class functions on domains with matrix polynomial defining function in \(\mathbb C^{n}\)
• Fundamental Agler decompositions
• Properties of compressed shifts on Beurling type quotient module of Hardy space over the bidisk
• The reducibility of compressed shifts on a class of quotient modules over the bidisk
• The reducibility of compressed shifts on Beurling type quotient modules over the bidisk
• Schur-Agler and Herglotz-Agler classes of functions: positive-kernel decompositions and transfer-function realizations
• Inner functions on the bidisk and associated Hilbert spaces
• Scattering systems with several evolutions and multidimensional input/state/output systems
• Harmonic analysis of operators on Hilbert space
• Properties of vector-valued submodules on the bidisk
• On a Class of Operators
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