Spectral synthesis for $A(G)$ and subspaces of $VN(G)$

DOI10.1090/S0002-9939-01-05924-XzbMath0976.43002OpenAlexW1522723155MaRDI QIDQ2731917

Anthony To-Ming Lau, Eberhard Kaniuth

Publication date: 30 July 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-01-05924-x

zbMATH Keywords

von Neumann algebralocally compact groupFourier algebra\(X\)-Ditkin set\(X\)-spectral set

Mathematics Subject Classification ID

Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) (43A46) Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. (43A30) Spectral synthesis on groups, semigroups, etc. (43A45) Group algebras of locally compact groups (22D15)

Related Items

Operator synthesis. I: Synthetic sets, bilattices and tensor algebras ⋮ On ideals of L1-algebras of compact quantum groups ⋮ Reduced spectral synthesis and compact operator synthesis ⋮ On character amenability of the Fourier algebra ⋮ Ideals of the Fourier algebra, supports and harmonic operators ⋮ Amenability, weak amenability and bounded approximate identities in multipliers of the Fourier algebra ⋮ Fourier algebras on homogeneous spaces ⋮ Power boundedness in Fourier and Fourier-Stieltjes algebras and other commutative Banach algebras ⋮ Helson Sets of Synthesis Are Ditkin Sets ⋮ Ideals with bounded approximate identities in Fourier algebras. ⋮ Malliavin's theorem for weak synthesis on nonabelian groups ⋮ Spectral synthesis in the Fourier algebra and the Varopoulos algebra ⋮ Weak spectral synthesis in commutative Banach algebras ⋮ Homological properties of Fourier algebras on homogeneous spaces ⋮ Weak spectral synthesis in commutative Banach algebras. II. ⋮ Ideals of \(A(G)\) and bimodules over maximal abelian selfadjoint algebras ⋮ An extension property for the Figà-Talamanca Herz algebra ⋮ A separation property of positive definite functions on locally compact groups and applications to Fourier algebras ⋮ Spectral synthesis and topologies on ideal spaces for Banach \(^{*}\)-algebras ⋮ Strong Ditkin sets in the spectrum of a commutative Banach algebra and the Fourier algebra

Cites Work

• Unnamed Item
• Unnamed Item
• Impossibilité de la synthèse spectrale sur les groupes abéliens non compacts
• Quelques observations concernant les ensembles de Ditkin d'un groupe localement compact. (Ditkin sets on locally compact groups)
• The \(C^ \ast\)-algebra generated by operators with compact support on a locally compact group
• Fourier analysis on coset spaces
• On periodic compact groups
• Duality and subgroups. II
• Remarques sur les ensembles de synthese des algèbres de groupe localement compact
• Harmonic synthesis for subgroups
• Contributions to harmonic analysis. VI
• The Spectral Theory of Bounded Functions
• Almost Periodic Operators in VN(G)
• On the union of sets of synthesis and Ditkin’s condition in regular Banach algebras
• Uniformly Continuous Functionals on the Fourier Algebra of Any Locally Compact Group
• Weakly Almost Periodic and Uniformly Continuous Functionals on the Fourier Algebra of any Locally Compact Group
• A Class of Spectral Sets
• Weak*-closedness of subspaces of Fourier-Stieltjes algebras and weak*-continuity of the restriction map
• L'algèbre de Fourier d'un groupe localement compact
• Extensions of positive-definite functions