Nearly invariant subspaces for operators in Hilbert spaces

2020/03/27 by Yu‐Xia Liang, Liang, Yuxia, J. R. Partington +1 · 3 citations
Mathematics · #47A15 #47B38 #Advanced Operator Algebra Research #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.2003.12549

openalex publication_date 2020/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a shift operator T with finite multiplicity acting on a separable infinite dimensional Hilbert space we represent its nearly T^-1 invariant subspaces in terms of invariant subspaces under the backward shift. Going further, given any finite Blaschke product B, we give a description of the nearly T_B^-1 invariant subspaces for the operator T_B of multiplication by B in a scale of Dirichlet-type spaces.

Cited by

• Near Invariance of The Dual Compressed Shift
• Perturbations of Toeplitz operators on vector-valued Hardy spaces
• Spectra and invariant subspaces of compressed shifts on nearly invariant subspaces

Related

• Study of nearly invariant subspaces with finite defect in Hilbert spaces
• Almost invariant subspaces of shift operators and products of Toeplitz and Hankel operators
• Invariant subspaces of perturbed backward shift
• Almost invariant half-spaces of operators on Banach spaces
• A Beurling Theorem for almost-invariant subspaces of the shift operator