scholarly journals Multinorms and Approximate Amenability of Weighted Group Algebras

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Saman Ghaderkhani
Keyword(s):  
Weight Function ◽  
Compact Group ◽  
Banach Algebra ◽  
Locally Compact Group ◽  
Group Algebras ◽  
Locally Compact ◽  
Approximate Amenability

Let G be a locally compact group, and take p,q with 1≤p,q<∞. We prove that, for any left (p,q)-multiinvariant functional on L∞(G) and for any weight function ω≥1 on G, the approximate amenability of the Banach algebra L1(G,ω) implies the left (p,q)-amenability of G, but in general the opposite is not true. Our proof uses the notion of multinorms. We also investigate the approximate amenability of M(G,ω).

scholarly journals META-CENTRALIZERS OF NON-LOCALLY COMPACT GROUP ALGEBRAS

2014 ◽  
Vol 57 (2) ◽  
pp. 349-364 ◽  
Author(s):  
S. V. LUDKOVSKY
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Group Algebras ◽  
Locally Compact

AbstractMeta-centralizers of non-locally compact group algebras are studied. Theorems about their representations with the help of families of generalized measures are proved. Isomorphisms of group algebras are investigated in relation with meta-centralizers.

scholarly journals Amenability and semisimplicity for second duals of quotients of the Fourier algebraA(G)

1997 ◽  
Vol 63 (3) ◽  
pp. 289-296 ◽  
Author(s):  
Edmond E. Granirer
Keyword(s):  
Compact Group ◽  
Banach Algebra ◽  
Closed Subgroup ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Amenable Banach Algebra ◽  
Symmetric Set ◽  
Semisimple Banach Algebra

AbstractLetF ⊂ Gbe closed andA(F) = A(G)/IF. IfFis a Helson set thenA(F)**is an amenable (semisimple) Banach algebra. Our main result implies the following theorem: LetGbe a locally compact group,F ⊂ Gclosed,a ∈ G. Assume either (a) For some non-discrete closed subgroupH, the interior ofF ∩ aHinaHis non-empty, or (b)R ⊂ G, S ⊂ Ris a symmetric set andaS ⊂ F. ThenA(F)**is a non-amenable non-semisimple Banach algebra. This raises the question: How ‘thin’ canFbe forA(F)**to remain a non-amenable Banach algebra?

Unit Elements in the Double Dual of a Subalgebra of the Fourier Algebra A(G)

2009 ◽  
Vol 61 (2) ◽  
pp. 382-394
Author(s):  
Tianxuan Miao
Keyword(s):  
Compact Group ◽  
Banach Algebra ◽  
Locally Compact Group ◽  
Approximate Identity ◽  
Fourier Algebra ◽  
Locally Compact ◽  
Arens Product ◽  
The Right ◽  
Topological Centers ◽  
The Relationship

Abstract. Let 𝒜 be a Banach algebra with a bounded right approximate identity and let ℬ be a closed ideal of 𝒜. We study the relationship between the right identities of the double duals ℬ** and 𝒜** under the Arens product. We show that every right identity of ℬ** can be extended to a right identity of 𝒜** in some sense. As a consequence, we answer a question of Lau and Ülger, showing that for the Fourier algebra A(G) of a locally compact group G, an element ϕ ∈ A(G)** is in A(G) if and only if A(G)ϕ ⊆ A(G) and Eϕ = ϕ for all right identities E of A(G)**. We also prove some results about the topological centers of ℬ** and 𝒜**.

scholarly journals AN ARBITRARY INTERSECTION OF Lp-SPACES

2012 ◽  
Vol 85 (3) ◽  
pp. 433-445 ◽  
Author(s):  
F. ABTAHI ◽  
H. G. AMINI ◽  
H. A. LOTFI ◽  
A. REJALI
Keyword(s):  
Banach Space ◽  
Compact Group ◽  
Banach Algebra ◽  
Locally Compact Group ◽  
Convolution Product ◽  
Special Choice ◽  
Arbitrary Subset ◽  
Locally Compact ◽  
Lp Spaces ◽  
Algebraic Properties

AbstractFor a locally compact group G and an arbitrary subset J of [1,∞], we introduce ILJ(G) as a subspace of ⋂ p∈JLp(G) with some norm to make it a Banach space. Then, for some special choice of J, we investigate some topological and algebraic properties of ILJ(G) as a Banach algebra under a convolution product.

scholarly journals On Cauchy-type functional equations

2004 ◽  
Vol 2004 (16) ◽  
pp. 847-859
Author(s):  
Elqorachi Elhoucien ◽  
Mohamed Akkouchi
Keyword(s):  
Compact Group ◽  
Banach Algebra ◽  
Functional Equations ◽  
Continuous Functions ◽  
Locally Compact Group ◽  
Cauchy Type ◽  
Matrix Functions ◽  
Continuous Solutions ◽  
Locally Compact

LetGbe a Hausdorff topological locally compact group. LetM(G)denote the Banach algebra of all complex and bounded measures onG. For all integersn≥1and allμ∈M(G), we consider the functional equations∫Gf(xty)dμ(t)=∑i=1ngi(x)hi(y),x,y∈G, where the functionsf,{gi},{hi}:G→ℂto be determined are bounded and continuous functions onG. We show how the solutions of these equations are closely related to the solutions of theμ-spherical matrix functions. WhenGis a compact group andμis a Gelfand measure, we give the set of continuous solutions of these equations.

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 The continuity of derivations from group algebras: factorizable and connected groups

1992 ◽  
Vol 52 (2) ◽  
pp. 185-204 ◽  
Author(s):  
George Willis
Keyword(s):  
Finite Number ◽  
Compact Group ◽  
Locally Compact Group ◽  
Group Algebras ◽  
Locally Compact ◽  
Abelian Subgroups

AbstractA group is said to be factorizable if it has a finite number of abelian subgroups, H1, H2, … Hn, such that G = H1H2 … Hn. It is shown that, if G is a factorizable or connected locally compact group, then every derivation from L1 (G) to an arbitrary L1 (G)-bimodule X is continuous.

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.

Isomorphisms between the second duals of group algebras of locally compact groups

1996 ◽  
Vol 119 (4) ◽  
pp. 657-663 ◽  
Author(s):  
Hamid-Reza Farhadi
Keyword(s):  
Compact Group ◽  
Group Algebra ◽  
Locally Compact Group ◽  
Group Algebras ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Algebra Isomorphism ◽  
Continuous Automorphism

AbstractLet G be a locally compact group and L1(G) be the group algebra of G. We show that G is abelian or compact if every continuous automorphism of L1(G)** maps L1(G) onto L1(G) This characterizes all groups with this property and answers a question raised by F. Ghahramani and A. T. Lau in [7]. We also show that if G is a compact group and θ is any (algebra) isomorphism from L1(G)** onto L1(H)**, then H is compact and θ maps L1(G) onto L1(H).

Weak*- continuous homomorphisms of Fourier–Stieltjes algebras

2008 ◽  
Vol 145 (1) ◽  
pp. 107-120 ◽  
Author(s):  
MONICA ILIE ◽  
ROSS STOKKE
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Group Algebras ◽  
Algebra Homomorphism ◽  
Affine Mapping ◽  
Locally Compact ◽  
Amenable Groups ◽  
Affine Map ◽  
Piecewise Affine ◽  
Open Map

AbstractFor a locally compact group G, let B(G) denote its Fourier–Stieltjes algebra. Any continuous, piecewise affine map α: Y ⊂ H → G induces a completely bounded algebra homomorphism jα: B(G) → B(H) [14, 15] and we prove that jα is w* – w* continuous if and only if α is an open map. This extends one of the main results in [3], due to M.B. Bekka, E. Kaniuth, A.T. Lau and G. Schlichting. Several classical theorems regarding isomorphisms and extensions of homomorphisms on group algebras of abelian groups are extended to the setting of Fourier–Stieltjes algebras of amenable groups. As applications, when G is amenable we provide complete characterizations of those maps between Fourier–Stieltjes algebras that are either associated to a piecewise affine mapping, or are completely bounded and w* – w* continuous.

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