Shift invariant subspaces with arbitrary indices in \(\ell^p\) spaces

DOI10.1006/jfan.2001.3850zbMath1016.47008OpenAlexW2033541608MaRDI QIDQ1604541

Alexander Borichev, Evgeny V. Abakumov

Publication date: 4 July 2002

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.2001.3850

zbMATH Keywords

index of an invariant subspaceBanach spaces of weighted sequencescyclic multiplicity

Mathematics Subject Classification ID

Invariant subspaces of linear operators (47A15) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37)

Related Items (10)

Sampling and interpolation in large Bergman and Fock spaces ⋮ Zeros of optimal polynomial approximants in \(\ell_A^p\) ⋮ Zero-based subspaces and quasi-invariant subspaces of the Bargmann-Fock space ⋮ Large Bergman spaces: Invertibility, cyclicity, and subspaces of arbitrary index. ⋮ Invariant subspaces of arbitrary multiplicity for the shift on $\ell ^1$ ⋮ Multipliers of sequence spaces ⋮ Maximal, minimal, and primary invariant subspaces ⋮ An inner-outer factorization in \(\ell^{p}\) with applications to ARMA processes ⋮ Inner functions and zero sets for ℓ^{𝑝}_{𝐴} ⋮ On the failure of canonical factorization in \(\ell_A^p\)

Cites Work

• Invariant subspaces, dilation theory, and the structure of the predual of a dual algebra. I
• Linear and complex analysis problem book 3. Part 2
• Completeness of translates in weighted spaces on the half-line
• Beurling's theorem for the Bergman space
• Cyclicity and approximation by lacunary power series
• On two problems concerning linear transformations in Hilbert space
• Invariant subspaces of arbitrary multiplicity for the shift on $\ell ^1$
• An invariant subspace of the Bergman space having the codimension two property.
• Invariant Subspaces in Banach Spaces of Analytic Functions
• Pseudocontinuations and the backward shift
• Sous-espaces invariants par translations bilatérales de certains espaces de Hilbert de suites quasi-analytiquement pondérées
• Invariant subspaces of given index in Banach spaces of analytic functions

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