Amenability of compact hypergroup algebras

2014 ◽  
Vol 287 (14-15) ◽  
pp. 1609-1617 ◽  
Author(s):  
Massoud Amini ◽  
Ali Reza Medghalchi
Keyword(s):  
Compact Hypergroup ◽  
Hypergroup Algebras

HYPERGROUP ALGEBRAS AS TOPOLOGICAL ALGEBRAS

2014 ◽  
Vol 90 (3) ◽  
pp. 486-493
Author(s):  
S. MAGHSOUDI ◽  
J. B. SEOANE-SEPÚLVEDA
Keyword(s):  
Haar Measure ◽  
Lebesgue Space ◽  
Topological Algebra ◽  
Topological Algebras ◽  
Locally Compact ◽  
Continuous Functionals ◽  
Locally Convex Topology ◽  
Compact Hypergroup ◽  
Locally Convex ◽  
Hypergroup Algebras

AbstractLet $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}K$ be a locally compact hypergroup endowed with a left Haar measure and let $L^1(K)$ be the usual Lebesgue space of $K$ with respect to the left Haar measure. We investigate some properties of $L^1(K)$ under a locally convex topology $\beta ^1$. Among other things, the semireflexivity of $(L^1(K), \beta ^1)$ and of sequentially$\beta ^1$-continuous functionals is studied. We also show that $(L^1(K), \beta ^1)$ with the convolution multiplication is always a complete semitopological algebra, whereas it is a topological algebra if and only if $K$ is compact.

scholarly journals Hypergroups and hypergroup algebras

1987 ◽  
Vol 38 (2) ◽  
pp. 1734-1761 ◽  
Author(s):  
G. L. Litvinov
Keyword(s):  
Hypergroup Algebras

Compact multipliers on weighted hypergroup algebras. II

1986 ◽  
Vol 100 (1) ◽  
pp. 145-149 ◽  
Author(s):  
F. Ghahramani ◽  
A. R. Medgalchi
Keyword(s):  
General Setting ◽  
Positive Answer ◽  
Weakly Compact ◽  
Hypergroup Algebras

In [7] we gave a description of compact multipliers of Lω(X), and left open the question of whether weakly compact multipliers on Lω(X) are compact. This had already been answered for some examples of hypergroup algebras ([1], [2], [6] and [10]). Here we give a positive answer to this question in the general setting of a weighted hypergroup algebra.

Cohomology on hypergroup algebras

2002 ◽  
Vol 39 (3-4) ◽  
pp. 297-307
Author(s):  
A. R. Medghalchi
Keyword(s):  
Topological Group ◽  
Banach Algebra ◽  
Group Algebra ◽  
Linear Functional ◽  
Approximate Identity ◽  
Invariant Mean ◽  
Augmentation Ideal ◽  
Dual Module ◽  
Hypergroup Algebras

There are concepts which are related to or can be formulated by homological techniques, such as derivations, multipliers and lifting problems. Moreover, a Banach algebra A is said to be amenable if H1(A,X*)=0 for every A-dual module X*. Another concept related to the theory is the concept of amenability in the sense of Johnson. A topological group G is said to be amenable if there is an invariant mean on L 8(G). Johnson has shown that a topological group is amenable if and only if the group algebra L1(G) is amenable. The aim of this research is to define the cohomology on a hypergroup algebra L(K) and extend the results of L1(G) over to L(K). At first stage it is viewed that Johnson's theorem is not valid so more. If A is a Banach algebra and h is a multiplicative linear functional on A, then (A,h) is called left amenable if for any Banach two-sided A-module X with ax=h(a)x(a? A, x? X),H1(A,X*)=0. We prove that (L(K),h) is left amenable if and only if K is left amenable. Where, the latter means that there is a left invariant mean m on C(K), i. e., m(lf)=m(f)x, where lxf(µ)=f(dx*µ). In this case we briefly say that L(K) is left amenable. Johnson also showed that L1(G) is amenable if and only if the augmentation ideal I={f? L1(G)|∫Gf=0}0 has abounded right approximate identity. We extend this result to hypergroups.

Compact multipliers on weighted hypergroup algebras

1985 ◽  
Vol 98 (3) ◽  
pp. 493-500 ◽  
Author(s):  
F. Ghahramani ◽  
A. R. Medgalchi
Keyword(s):  
Banach Algebra ◽  
Group Algebras ◽  
Semigroup Algebras ◽  
Weighted Semigroup ◽  
Hypergroup Algebras

AbstractLet Mω(X) be a weighted hypergroup algebra, and Lω(X) be the Banach algebra of measures μ ε Mω(X) such that the function x ↦ (1/ω(x))δx* |μ| is norm continuous. We characterize compact multipliers on Lω(X). This extends the characterization of compact multipliers on weighted group algebras and some classes of weighted semigroup algebras.

scholarly journals Generalized hypergroups and orthogonal polynomials

1996 ◽  
Vol 142 ◽  
pp. 67-93 ◽  
Author(s):  
Nobuaki Obata ◽  
Norman J. Wildberger
Keyword(s):  
Orthogonal Polynomials ◽  
Harmonic Analysis ◽  
Abelian Groups ◽  
Locally Compact ◽  
Locally Compact Abelian Groups ◽  
Convolution Algebras ◽  
Compact Abelian Groups ◽  
Compact Hypergroup

We study in this paper a generalization of the notion of a discrete hypergroup with particular emphasis on the relation with systems of orthogonal polynomials. The concept of a locally compact hypergroup was introduced by Dunkl [8], Jewett [12] and Spector [25]. It generalizes convolution algebras of measures associated to groups as well as linearization formulae of classical families of orthogonal polynomials, and many results of harmonic analysis on locally compact abelian groups can be carried over to the case of commutative hypergroups; see Heyer [11], Litvinov [17], Ross [22], and references cited therein. Orthogonal polynomials have been studied in terms of hypergroups by Lasser [15] and Voit [31], see also the works of Connett and Schwartz [6] and Schwartz [23] where a similar spirit is observed.

Characters of induced representations of a compact hypergroup

2015 ◽  
Vol 179 (3) ◽  
pp. 421-440 ◽  
Author(s):  
Herbert Heyer ◽  
Satoshi Kawakami ◽  
Satoe Yamanaka
Keyword(s):  
Induced Representations ◽  
Compact Hypergroup
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