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 Some Intersections of the Weighted -Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
F. Abtahi ◽  
H. G. Amini ◽  
H. A. Lotfi ◽  
A. Rejali
Keyword(s):  
Banach Space ◽  
Sufficient Conditions ◽  
Locally Convex Space ◽  
Locally Compact Group ◽  
Weight Functions ◽  
Convolution Product ◽  
Arbitrary Subset ◽  
Locally Compact ◽  
Algebraic Properties ◽  
Locally Convex

Let be a locally compact group an arbitrary family of the weight functions on and . The locally convex space as a subspace of is defined. Also, some sufficient conditions for that space to be a Banach space are provided. Furthermore, for an arbitrary subset of and a positive submultiplicative weight function on , Banach subspace of is introduced. Then some algebraic properties of , as a Banach algebra under convolution product, are investigated.

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.

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 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 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 Biprojectivity and Biflatness for Convolution Algebras of Nuclear Operators

2004 ◽  
Vol 47 (3) ◽  
pp. 445-455 ◽  
Author(s):  
A. Yu. Pirkovskii
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Convolution Product ◽  
Locally Compact ◽  
Convolution Algebra ◽  
Nuclear Operators ◽  
Convolution Algebras

AbstractFor a locally compact group G, the convolution product on the space 𝒩(Lp(G)) of nuclear operators was defined by Neufang [11]. We study homological properties of the convolution algebra 𝒩(Lp(G)) and relate them to some properties of the group G, such as compactness, finiteness, discreteness, and amenability.

Predual of the Multiplier Algebra of Ap(G) and Amenability

2004 ◽  
Vol 56 (2) ◽  
pp. 344-355 ◽  
Author(s):  
Tianxuan Miao
Keyword(s):  
Banach Space ◽  
Compact Group ◽  
Linear Span ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Multiplier Algebra ◽  
Norm Closure ◽  
Multiplier Space ◽  
Dual Banach Space

AbstractFor a locally compact group G and 1 < p < ∞, let Ap(G) be the Herz-Figà-Talamanca algebra and let PMp(G) be its dual Banach space. For a Banach Ap(G)-module X of PMp(G), we prove that the multiplier space ℳ(Ap(G); X*) is the dual Banach space of QX, where QX is the norm closure of the linear span Ap(G)X of u f for u 2 Ap(G) and f ∈ X in the dual of ℳ(Ap(G); X*). If p = 2 and PFp(G) ⊆ X, then Ap(G)X is closed in X if and only if G is amenable. In particular, we prove that the multiplier algebra MAp(G) of Ap(G) is the dual of Q, where Q is the completion of L1(G) in the ‖ · ‖M-norm. Q is characterized by the following: f ∈ Q if an only if there are ui ∈ Ap(G) and fi ∈ PFp(G) (i = 1; 2, … ) with such that on MAp(G). It is also proved that if Ap(G) is dense in MAp(G) in the associated w*-topology, then the multiplier norm and ‖ · ‖Ap(G)-norm are equivalent on Ap(G) if and only if G is amenable.

scholarly journals On a Certain Class of Semigroups of Operators

2011 ◽  
Vol 18 (02) ◽  
pp. 129-142 ◽  
Author(s):  
Paolo Aniello
Keyword(s):  
Banach Space ◽  
Compact Group ◽  
Banach Spaces ◽  
Locally Compact Group ◽  
Semigroups Of Operators ◽  
Probability Measures ◽  
Locally Compact ◽  
Quantum Dynamical ◽  
Interesting Class ◽  
Natural Way

We define an interesting class of semigroups of operators in Banach spaces, namely, the randomly generated semigroups. This class contains as a remarkable subclass a special type of quantum dynamical semigroups introduced in the early 1970s by Kossakowski. Each randomly generated semigroup is associated, in a natural way, with a pair formed by a representation or an antirepresentation of a locally compact group in a Banach space and by a convolution semigroup of probability measures on this group. Examples of randomly generated semigroups having important applications in physics are briefly illustrated.

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