The existence of translation invariant subspaces of symmetric self-adjoint sequence spaces on \(\mathbb{Z}\)

DOI10.1006/jfan.2000.3660zbMath0978.47022OpenAlexW1997491082WikidataQ87990082 ScholiaQ87990082MaRDI QIDQ1840577

Aharon Atzmon

Publication date: 15 January 2002

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

Full work available at URL: https://doi.org/10.1006/jfan.2000.3660

zbMATH Keywords

Banach spaces of complex sequences on \(\mathbb{Z}\)translation invariant Banach spacetranslation invariant subspace problem

Mathematics Subject Classification ID

Invariant subspaces of linear operators (47A15) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) Banach sequence spaces (46B45)

Related Items (6)

Large Bergman spaces: Invertibility, cyclicity, and subspaces of arbitrary index. ⋮ Multipliers of weighted spaces and reflexivity property ⋮ Cyclicity of bicyclic operators and completeness of translates ⋮ Reducible representations of abelian groups ⋮ Invariant subspaces for tridiagonal operators. ⋮ Asymptotically holomorphic functions and translation invariant subspaces of weighted Hilbert spaces of sequences

Cites Work

• Singular inner functions and biinvariant subspaces for dissymmetric weighted shifts
• Hyperinvariant subspaces for bilateral weighted shifts
• Completely indecomposable operators and a uniqueness theorem of Cartwright-Levinson type: Addendum
• Completely indecomposable operators and a uniqueness theorem of Cartwright-Levinson type
• On Fourier transforms of measures with compact support
• Strict Convexity and Smoothness of Normed Spaces
• Sous-espaces invariants par translations bilatérales de certains espaces de Hilbert de suites quasi-analytiquement pondérées
• An Extension of Lomonosov’s Techniques to Non-compact Operators
• Translation invariant subspaces of weighted $l^p$ and $L^p$ spaces.
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