Cyclicity of bicyclic operators and completeness of translates

DOI10.1007/s00208-007-0191-2zbMath1185.47006OpenAlexW1984478706MaRDI QIDQ2482694

Evgeny V. Abakumov, Sophie Grivaux, Aharon Atzmon

Publication date: 23 April 2008

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-007-0191-2

zbMATH Keywords

shift operatorscyclic vectorsbicyclic vectors

Mathematics Subject Classification ID

Banach algebras of continuous functions, function algebras (46J10) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) Completeness of sets of functions in nontrigonometric harmonic analysis (42C30) Cyclic vectors, hypercyclic and chaotic operators (47A16) Quasi-analytic and other classes of functions of one complex variable (30D60) Completeness of sets of functions in one variable harmonic analysis (42A65)

Related Items (3)

Spans of translates in weighted \(\ell^p\) spaces ⋮ Cyclicity in \(\ell^{p}\) spaces and zero sets of the Fourier transforms ⋮ Operators admitting a closed subspace of cyclic vectors

Cites Work

• Singular inner functions and biinvariant subspaces for dissymmetric weighted shifts
• Harmonic analysis based on certain commutative Banach algebras
• Eigenvectors and cyclic vectors of bilateral weighted shifts. II: Simply invariant subspaces
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• On multicyclic operators
• The existence of translation invariant subspaces of symmetric self-adjoint sequence spaces on \(\mathbb{Z}\)
• Generating sets for Beurling algebras
• On translation and affine systems spanning \(L^{1}(\mathbb R)\)
• Subnormal operators
• Closed Primary Ideals in a Class of Banach Algebras.
• Universal families and hypercyclic operators
• The Curious History of Faa di Bruno's Formula
• Supercyclicity and weighted shifts
• Eigenvalues of Modulus 1
• Translation invariant subspaces of weighted $l^p$ and $L^p$ spaces.
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