Perturbations of Toeplitz operators on vector-valued Hardy spaces

2025/07/08 by Arshad Khan, Khan, Arshad, Sneh Lata +3 · 1 citation
Mathematics · #47A55 #47B35 #47B38 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary 47A15 #Secondary 30H10

paper · pdf · doi:10.48550/arxiv.2507.05721

openalex publication_date 2025/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we completely classify invariant subspaces of finite-rank perturbations of a class of Toeplitz operators on vector-valued Hardy spaces. As a consequence, in the vector-valued setting, we characterize invariant and almost invariant subspaces of a class of Toeplitz operators, as well as nearly invariant subspaces associated with certain Blaschke-based operators. We further treat the finite defect case for these nearly invariant subspaces.

Citations

• Invariant subspaces of perturbed backward shift
• Cyclic nearly invariant subspaces for semigroups of isometries
• Nearly invariant subspaces for shift semigroups
• Study of nearly invariant subspaces with finite defect in Hilbert spaces
• Kernels of Perturbed Toeplitz Operators in vector-valued Hardy spaces
• Almost invariant subspaces of the shift operator on vector-valued Hardy\n spaces
• Nearly invariant subspaces for operators in Hilbert spaces
• Representing kernels of perturbations of Toeplitz operators by backward shift-invariant subspaces
• A Beurling Theorem for almost-invariant subspaces of the shift operator

Cited by

• Near Invariance of The Dual Compressed Shift

Related

• Kernels of Perturbed Toeplitz Operators in vector-valued Hardy spaces
• Nearly invariant subspaces and kernels of Toeplitz operators on the Hardy space over the bidisk
• Invariant subspaces of perturbed backward shift
• Almost invariant subspaces of the shift operator on vector-valued Hardy\n spaces
• Schmidt subspaces of block Hankel operators