Inner sequence based invariant subspaces in H2(D2)

Michio Seto; Rongwei Yang

doi:10.1090/S0002-9939-07-08745-X

Inner sequence based invariant subspaces in H²(D²)

Michio Seto
, Rongwei Yang

Mathematics and Statistics

University at Albany

Kanagawa University

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

A closed subspace H² (D²) is said to be invariant if it is invariant under the Toeplitz operators T_z and T_w. Invariant subspaces of H² (D²) are well-known to be very complicated. So discovering some good examples of invariant subspaces will be beneficial to the general study. This paper studies a type of invariant subspace constructed through a sequence of inner functions. It will be shown that this type of invariant subspace has direct connections with the Jordan operator. Related calculations also give rise to a simple upper bound for Σ _j 1 - |λ_j|, where {λ_j} are zeros of a Blaschke product.

Original language	English
Pages (from-to)	2519-2526
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	135
Issue number	8
DOIs	https://doi.org/10.1090/S0002-9939-07-08745-X
State	Published - Aug 2007

Keywords

Blaschke product
Core operator
Hardy space over the bidisk
Jordan operator

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abstract = "A closed subspace H2 (D2) is said to be invariant if it is invariant under the Toeplitz operators Tz and Tw. Invariant subspaces of H2 (D2) are well-known to be very complicated. So discovering some good examples of invariant subspaces will be beneficial to the general study. This paper studies a type of invariant subspace constructed through a sequence of inner functions. It will be shown that this type of invariant subspace has direct connections with the Jordan operator. Related calculations also give rise to a simple upper bound for Σ j 1 - |λj|, where \{λj\} are zeros of a Blaschke product.",

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AB - A closed subspace H2 (D2) is said to be invariant if it is invariant under the Toeplitz operators Tz and Tw. Invariant subspaces of H2 (D2) are well-known to be very complicated. So discovering some good examples of invariant subspaces will be beneficial to the general study. This paper studies a type of invariant subspace constructed through a sequence of inner functions. It will be shown that this type of invariant subspace has direct connections with the Jordan operator. Related calculations also give rise to a simple upper bound for Σ j 1 - |λj|, where {λj} are zeros of a Blaschke product.

KW - Blaschke product

KW - Core operator

KW - Hardy space over the bidisk

KW - Jordan operator

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EP - 2526

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 8

ER -

Inner sequence based invariant subspaces in H²(D²)

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Keywords

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