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.

scholarly journals On isomorphisms between weighted -algebras

2020 ◽  
pp. 1-14
Author(s):  
Yulia Kuznetsova ◽  
Safoura Zadeh
Keyword(s):  
Compact Group ◽  
Composition Operators ◽  
Function Spaces ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Classical Function ◽  
Continuous Weight

Abstract Let G be a locally compact group and let $\omega $ be a continuous weight on G. In this paper, we first characterize bicontinuous biseparating algebra isomorphisms between weighted $L^p$ -algebras. As a result, we extend previous results of Edwards, Parrott, and Strichartz on algebra isomorphisms between $L^p$ -algebras to the setting of weighted $L^p$ -algebras. We then study the automorphisms of certain weighted $L^p$ -algebras on integers, applying known results on composition operators to classical function spaces.

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.

On invariant convex subsets in algebras defined on a locally compact group G

2012 ◽  
Vol 49 (3) ◽  
pp. 301-314
Author(s):  
Ali Ghaffari
Keyword(s):  
Compact Group ◽  
Sufficient Conditions ◽  
Locally Compact Group ◽  
Left Translation ◽  
Measure Algebra ◽  
Locally Compact ◽  
Translation Invariant ◽  
Second Dual ◽  
Necessary And Sufficient ◽  
Convex Subsets

Suppose that A is either the Banach algebra L1(G) of a locally compact group G, or measure algebra M(G), or other algebras (usually larger than L1(G) and M(G)) such as the second dual, L1(G)**, of L1(G) with an Arens product, or LUC(G)* with an Arenstype product. The left translation invariant closed convex subsets of A are studied. Finally, we obtain necessary and sufficient conditions for LUC(G)* to have 1-dimensional left ideals.

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.

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.

scholarly journals The modulus of operators on group algebras

2004 ◽  
Vol 35 (2) ◽  
pp. 95-100
Author(s):  
Ali. Ghaffari
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Group Algebras ◽  
Locally Compact ◽  
Second Dual

Let $ G $ be a locally compact group. In this paper, we study the modulus of right multipliers on second dual of group algebras and modulus of operators on $ L^\infty (G)$ which commute with convolutions.

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**.

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