Dual Banach algebras associated to the coset space of a locally compact group

2018 ◽  
Vol 467 (1) ◽  
pp. 550-569 ◽  
Author(s):  
Monica Ilie
Keyword(s):  
Compact Group ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Coset Space ◽  
Locally Compact

scholarly journals Johnson pseudo-Connes amenability of dual Banach algebras

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 551-559
Author(s):  
Amir Sahami ◽  
Seyedeh Shariati ◽  
Abdolrasoul Pourabbas
Keyword(s):  
Compact Group ◽  
Finite Index ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Hereditary Properties ◽  
Connes Amenability

We introduce the notion of Johnson pseudo-Connes amenability for dual Banach algebras. We study the relation between this new notion with the various notions of Connes amenability like Connes amenability, approximate Connes amenability and pseudo Connes amenability. We also investigate some hereditary properties of this new notion. We prove that for a locally compact group G,M(G) is Johnson pseudo-Connes amenable if and only if G is amenable. Also we show that for every non-empty set I,MI(C) under this new notion is forced to have a finite index. Finally, we provide some examples of certain dual Banach algebras and we study their Johnson pseudo-Connes amenability.

scholarly journals Approximate Connes-biprojectivity of dual Banach algebras

2020 ◽  
pp. 2150025
Author(s):  
A. Sahami ◽  
S. F. Shariati ◽  
A. Pourabbas
Keyword(s):  
Compact Group ◽  
Banach Algebra ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Convolution Product ◽  
Locally Compact ◽  
Triangular Banach Algebras ◽  
Connes Amenability

In this paper, we introduce a notion of approximate Connes-biprojectivity for dual Banach algebras. We study the relation between approximate Connes-biprojectivity, approximate Connes amenability and [Formula: see text]-Connes amenability. We propose a criterion to show that certain dual triangular Banach algebras are not approximately Connes-biprojective. Next, we show that for a locally compact group [Formula: see text], the Banach algebra [Formula: see text] is approximately Connes-biprojective if and only if [Formula: see text] is amenable. Finally, for an infinite commutative compact group [Formula: see text], we show that the Banach algebra [Formula: see text] with convolution product is approximately Connes-biprojective, but it is not Connes-biprojective.

scholarly journals Completely continuous elements of Banach algebras related to locally compact groups

2007 ◽  
Vol 76 (1) ◽  
pp. 49-54 ◽  
Author(s):  
M. J. Mehdipour ◽  
R. Nasr-Isfahani
Keyword(s):  
Banach Space ◽  
Compact Group ◽  
Banach Algebra ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Completely Continuous ◽  
Measurable Functions

Let G be a locally compact group and be the Banach space of all essentially bounded measurable functions on G vansihing an infinity. Here, we study some families of right completely continuous elements in the Banach algebra equipped with an Arens type product. As the main result, we show that has a certain right completely continuous element if and only if G is compact.

Bipositive Isomorphisms Between Beurling Algebras and Between their Second Dual Algebras

2017 ◽  
Vol 69 (1) ◽  
pp. 3-20 ◽  
Author(s):  
F. Ghahramani ◽  
S. Zadeh
Keyword(s):  
Compact Group ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Order Structure ◽  
Algebra Structure ◽  
Locally Compact ◽  
Second Dual ◽  
Beurling Algebras ◽  
Continuous Weight

AbstractLet G be a locally compact group and let ω be a continuous weight on G. We show that for each of the Banach algebras L1(G,ω ), M(G,ω ), LUC(G,ω -1)*, and L1(G, ω)**, the order structure combined with the algebra structure determines the weighted group.

Lp-spaces on locally compact groups

2014 ◽  
Vol 64 (4) ◽  
Author(s):  
H. Samea
Keyword(s):  
Compact Group ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Lp Spaces

AbstractIn this paper, some relations between L p-spaces on locally compact groups are found. Applying these results proves that for a locally compact group G, the convolution Banach algebras L p(G) ∩ L 1(G) (1 < p ≤ ∞), and A p(G) ∩ L 1(G) (1 < p < ∞) are amenable if and only if G is discrete and amenable.

Module Homomorphisms of the Dual Modules of Convolution Banach Algebras

1992 ◽  
Vol 35 (2) ◽  
pp. 180-185 ◽  
Author(s):  
F. Ghahramani ◽  
J. P. Mcclure
Keyword(s):  
Compact Group ◽  
Group Algebra ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Banach Module ◽  
Locally Compact ◽  
Arens Product ◽  
Convolution Algebra

AbstractSuppose that A is either the group algebra L1 (G) of a locally compact group G, or the Volterra algebra or a weighted convolution algebra with a regulated weight. We characterize: a) Module homomorphisms of A*, when A* is regarded an A** left Banach module with the Arens product, b) all the weak*-weak* continuous left multipliers of A**.

scholarly journals COMPACT LEFT MULTIPLIERS ON BANACH ALGEBRAS RELATED TO LOCALLY COMPACT GROUPS

2009 ◽  
Vol 79 (2) ◽  
pp. 227-238 ◽  
Author(s):  
M. J. MEHDIPOUR ◽  
R. NASR-ISFAHANI
Keyword(s):  
Compact Group ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Completely Continuous ◽  
Left Multiplier

AbstractWe deal with the dual Banach algebras $L_0^\infty (G)^*$ for a locally compact group G. We investigate compact left multipliers on $L_0^\infty (G)^*$, and prove that the existence of a compact left multiplier on $L_0^\infty (G)^*$ is equivalent to compactness of G. We also describe some classes of left completely continuous elements in $L_0^\infty (G)^*$.

On the amenability of a class of Banach algebras with application to measure algebra

2019 ◽  
Vol 69 (5) ◽  
pp. 1177-1184
Author(s):  
Mohammad Reza Ghanei ◽  
Mehdi Nemati
Keyword(s):  
Compact Group ◽  
Invariant Subspace ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Approximate Identity ◽  
Invariant Mean ◽  
Measure Algebra ◽  
Locally Compact ◽  
Invariant Means ◽  
Inner Amenability

Abstract Let 𝓛 be a Lau algebra and X be a topologically invariant subspace of 𝓛* containing UC(𝓛). We prove that if 𝓛 has a bounded approximate identity, then strict inner amenability of 𝓛 is equivalent to the existence of a strictly inner invariant mean on X. We also show that when 𝓛 is inner amenable the cardinality of the set of topologically left invariant means on 𝓛* is equal to the cardinality of the set of topologically left invariant means on RUC(𝓛). Applying this result, we prove that if 𝓛 is inner amenable and 〈𝓛2〉 = 𝓛, then the essential left amenability of 𝓛 is equivalent to the left amenability of 𝓛. Finally, for a locally compact group G, we consider the measure algebra M(G) to study strict inner amenability of M(G) and its relation with inner amenability of G.

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