The norm-strict bidual of a Banach algebra and the dual of Cu(G)

DOI10.1007/BF01169770zbMath0527.46037MaRDI QIDQ786367

Viktor Losert, Michael Grosser

Publication date: 1984

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/154979

zbMATH Keywords

Banach algebracentergroup algebraBanach moduleArens productstrict topologyconvolution algebranorm-strict bidualspace of bounded uniformly continuous functions on an abelian locally compact Hausdorff group

Mathematics Subject Classification ID

Homomorphisms and multipliers of function spaces on groups, semigroups, etc. (43A22) General theory of topological algebras (46H05) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25) Group algebras of locally compact groups (22D15) Measure algebras on groups, semigroups, etc. (43A10)

Related Items (21)

Weakly compact multipliers on group algebras ⋮ Continuity of Arens multiplication on the dual space of bounded uniformly continuous functions on locally compact groups and topological semigroups ⋮ Isomorphisms and multipliers on second dual algebras of Banach algebras ⋮ The ideal structure of some Banach algebras ⋮ On the topological centre of the algebra \(\mathrm{LUC}({\mathcal G})^*\) for general topological groups ⋮ Certain strict topologies on the space of regular Borel measures on locally compact groups ⋮ Module maps on duals of Banach algebras and topological centre problems ⋮ The topological center of weighted semigroup algebras with a strict topology ⋮ Involutions and trivolutions in algebras related to second duals of group algebras ⋮ Topological centers of certain dual algebras ⋮ Some properties of \(LUC({\mathcal X},{\mathcal G})^*\) as a Banach left \(LUC({\mathcal G})^*\)-module ⋮ Banach algebras on semigroups and on their compactifications ⋮ THE STRONG DUAL OF MEASURE ALGEBRAS WITH CERTAIN LOCALLY CONVEX TOPOLOGIES ⋮ Joint continuity of multiplication on the dual of the left uniformly continuous functions ⋮ Slowly oscillating functions in semigroup compactifications and convolution algebras ⋮ Extreme non-Arens regularity of the group algebra ⋮ Isometric Isomorphisms Between Banach Algebras Related to Locally Compact Groups ⋮ Topological centres of weighted convolution algebras ⋮ On topological centre problems and SIN quantum groups ⋮ On the spectra of \(C^\ast\)-algebras of slowly oscillating functions on locally compact groups ⋮ Algebra involutions on the bidual of a Banach algebra

Cites Work

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• The center of the convolution algebra \(C_u(G)\)
• Multipliers on a Banach algebra with a bounded approximate identity
• The second conjugate space of a Banach algebra as an algebra
• Operations induced in function classes
• Left centralizers and isomorphisms of group algebras
• L 1 (G) as an Ideal in its Second Dual Space
• Dixmier's Representation Theorem of Central Double Centralizers on Banach Algebras
• Multipliers on Banach algebras
• The center of an algebra of operators
• Group Algebra Modules. I
• Factorization in Banach Algebras and the General Strict Topology
• The Strict Topology for Double Centralizer Algebras
• THE IRREGULARITY OF MULTIPLICATION IN GROUP ALGEBRAS
• The Adjoint of a Bilinear Operation

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