scholarly journals The radical of the bidual of a Beurling algebra

2018 ◽  
Vol 69 (3) ◽  
pp. 975-993
Author(s):  
Jared T White
Keyword(s):  
Beurling Algebra

scholarly journals On a family of weighted convolution algebras

1990 ◽  
Vol 13 (3) ◽  
pp. 517-525 ◽  
Author(s):  
Hans G. Feichtinger ◽  
A. Turan Gürkanli
Keyword(s):  
Fourier Transforms ◽  
Locally Compact Abelian Group ◽  
Asymptotic Estimates ◽  
Locally Compact ◽  
Invariance Properties ◽  
Beurling Algebra ◽  
Convolution Algebras ◽  
Approximate Identities ◽  
Beurling Algebras ◽  
Banach Ideals

Continuing a line of research initiated by Larsen, Liu and Wang [12], Martin and Yap [13], Gürkanli [15], and influenced by Reiter's presentation of Beurling and Segal algebras in Reiter [2,10] this paper presents the study of a family of Banach ideals of Beurling algebrasLw1(G),Ga locally compact Abelian group. These spaces are defined by weightedLp-conditions of their Fourier transforms. In the first section invariance properties and asymptotic estimates for the translation and modulation operators are given. Using these it is possible to characterize inclusions in section 3 and to show that two spaces of this type coincide if and only if their parameters are equal. In section 4 the existence of approximate identities in these algebras is established, from which, among other consequences, the bijection between the closed ideals of these algebras and those of the corresponding Beurling algebra is derived.

scholarly journals GENERALIZED AMENABILITY PROPERTIES OF THE BEURLING ALGEBRAS

2010 ◽  
Vol 89 (3) ◽  
pp. 359-376 ◽  
Author(s):  
F. GHAHRAMANI ◽  
E. SAMEI ◽  
YONG ZHANG
Keyword(s):  
Growth Condition ◽  
Slight Modification ◽  
Complete Characterization ◽  
Approximate Identity ◽  
Locally Compact Abelian Group ◽  
Weak Amenability ◽  
Beurling Algebra ◽  
Beurling Algebras ◽  
Approximate Amenability

AbstractWe show that every one-codimensional closed two-sided ideal in a boundedly approximately contractible Banach algebra has a bounded approximate identity. We use this to give a complete characterization of bounded approximate contractibility of Beurling algebras associated to symmetric weights. We give a slight modification of a criterion for bounded approximate contractibility. We use our criterion to show that, for the quasi-SIN groups, in the presence of a certain growth condition on a weight, the associated Beurling algebra is boundedly approximately amenable if and only if it is boundedly approximately contractible. We show that approximate amenability of a Beurling algebra on an IN group necessitates the amenability of the group. Finally, we show that, for every locally compact abelian group, in the presence of a growth condition on the weight, 2n-weak amenability of the associated Beurling algebra is equivalent to every point-derivation vanishing at the augmentation character.

scholarly journals Polynomials and functions with finite spectra on locally compact Abelian groups

1995 ◽  
Vol 51 (1) ◽  
pp. 33-42 ◽  
Author(s):  
B. Basit ◽  
A.J. Pryde
Keyword(s):  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Finite Spectrum ◽  
Beurling Algebra ◽  
Uniformly Continuous Function ◽  
Compact Abelian Groups ◽  
Indefinite Integral ◽  
Beurling Algebras ◽  
Primary Ideals ◽  
Uniformly Continuous

In this paper we define polynomials on a locally compact Abelian group G and prove the equivalence of our definition with that of Domar. We explore the properties of polynomials and determine their spectra. We also characterise the primary ideals of certain Beurling algebras on the group of integers Z. This allows us to classify those elements of that have finite spectrum. If ϕ is a uniformly continuous function with bounded differences then there is a Beurling algebra naturally associated with ϕ. We give a condition on the spectrum of ϕ relative to this algebra which ensures that ϕ is bounded. Finally we give spectral conditions on a bounded function on ℝ that ensure that its indefinite integral is bounded.

THE MULTIPLIER ALGEBRA OF A BEURLING ALGEBRA

2014 ◽  
Vol 90 (1) ◽  
pp. 113-120 ◽  
Author(s):  
S. J. BHATT ◽  
P. A. DABHI ◽  
H. V. DEDANIA
Keyword(s):  
Weight Function ◽  
Cancellative Semigroup ◽  
Multiplier Algebra ◽  
Beurling Algebra

AbstractFor a discrete abelian cancellative semigroup $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}S$ with a weight function $\omega $ and associated multiplier semigroup $M_\omega (S)$ consisting of $\omega $-bounded multipliers, the multiplier algebra of the Beurling algebra of $(S,\omega )$ coincides with the Beurling algebra of $M_\omega (S)$ with the induced weight.

scholarly journals A Beurling algebra is semisimple: an elementary proof

2002 ◽  
Vol 66 (1) ◽  
pp. 91-93 ◽  
Author(s):  
S. J. Bhatt ◽  
H. V. Dedania
Keyword(s):  
Abelian Group ◽  
Compact Abelian Group ◽  
Elementary Proof ◽  
Abelian Groups ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Beurling Algebra

The Beurling algebra L1(G,ω)on a locally compact Abelian group G with a measurable weight ω is shown to be semisimple. This gives an elementary proof of a result that is implicit in the work of M.C. White (1991), where the arguments are based on amenable (not necessarily Abelian) groups.

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