The Wiener–Pitt phenomenon on semi-groups

1963 ◽  
Vol 59 (1) ◽  
pp. 11-24 ◽  
Author(s):  
T. A. Davis
Keyword(s):  
Abelian Group ◽  
Banach Algebra ◽  
Haar Measure ◽  
Group Algebra ◽  
Compact Abelian Group ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Bounded Complex ◽  
Additive Measures ◽  
Complex Valued

Let G be a locally compact Abelian group, written adoptively, with Haar measure m, L1(G) the group algebra of G, and M(G) the Banach algebra of all bounded, complex-valued, regular, countably additive measures on G. For a general account of L1(G) and M(G) see Rudin (7).

On Multipliers of the Group Lp;w(G)-Algebras

2013 ◽  
Vol 59 (2) ◽  
pp. 253-268
Author(s):  
Ilker Eryilmaz ◽  
Cenap Duyar
Keyword(s):  
Abelian Group ◽  
Banach Algebra ◽  
Haar Measure ◽  
Compact Abelian Group ◽  
Locally Compact Abelian Group ◽  
Locally Compact

Abstract Let G be a locally compact abelian group (non-compact, non-discrete) with Haar measure and 1 ≤ p < ∞: The purpose of this paper is to study the space of multipliers on Lp;w (G) and characterize it as the algebra of all multipliers of the closely related Banach algebra of tempered elements in Lp;w (G).

On multipliers of Fourier transforms

1972 ◽  
Vol 71 (1) ◽  
pp. 63-66 ◽  
Author(s):  
Louis Pigno
Keyword(s):  
Abelian Group ◽  
Haar Measure ◽  
Compact Abelian Group ◽  
Lebesgue Space ◽  
Fourier Transforms ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Continuous Complex ◽  
Complex Valued

In this paper G is a locally compact Abelian group, φ a complex-valued function defined on the dual Γ, Lp(G) (1 ≤ p ≤ ∞) the usual Lebesgue space of index p formed with respect to Haar measure, C(G) the set of all bounded continuous complex-valued functions on G, and C0(G) the set of all f ∈ C(G) which vanish at infinity.

scholarly journals Tensor products of commutative Banach algebras

1982 ◽  
Vol 5 (3) ◽  
pp. 503-512
Author(s):  
U. B. Tewari ◽  
M. Dutta ◽  
Shobha Madan
Keyword(s):  
Abelian Group ◽  
Banach Algebra ◽  
Group Algebra ◽  
Compact Abelian Group ◽  
Banach Algebras ◽  
Locally Compact Abelian Group ◽  
Measure Algebra ◽  
Locally Compact ◽  
Integrable Functions ◽  
Commutative Banach Algebras

LetA1,A2be commutative semisimple Banach algebras andA1⊗∂A2be their projective tensor product. We prove that, ifA1⊗∂A2is a group algebra (measure algebra) of a locally compact abelian group, then so areA1andA2. As a consequence, we prove that, ifGis a locally compact abelian group andAis a comutative semi-simple Banach algebra, then the Banach algebraL1(G,A)ofA-valued Bochner integrable functions onGis a group algebra if and only ifAis a group algebra. Furthermore, ifAhas the Radon-Nikodym property, then the Banach algebraM(G,A)ofA-valued regular Borel measures of bounded variation onGis a measure algebra only ifAis a measure algebra.

scholarly journals A Theorem on Algebras of Measures on Topological Groups

1959 ◽  
Vol 11 (4) ◽  
pp. 195-206 ◽  
Author(s):  
J. H. Williamson
Keyword(s):  
Banach Space ◽  
Abelian Group ◽  
Compact Abelian Group ◽  
Locally Compact Abelian Group ◽  
Topological Groups ◽  
Finite Sets ◽  
Locally Compact ◽  
Borel Measures ◽  
Bounded Complex ◽  
Image Position

Let G be a locally compact Abelian group, and the set of bounded complex (regular countably-additive Borel) measures on G. It is well known that becomes a Banach space if the norm is defined bythe supremum being over all finite sets of disjoint Borel subsets of G.

scholarly journals On weak spectral synthesis

1991 ◽  
Vol 43 (2) ◽  
pp. 279-282 ◽  
Author(s):  
K. Parthasarathy ◽  
Sujatha Varma
Keyword(s):  
Abelian Group ◽  
Group Algebra ◽  
Lie Group ◽  
Compact Abelian Group ◽  
Spectral Synthesis ◽  
Locally Compact Abelian Group ◽  
Fourier Algebra ◽  
Compact Lie Group ◽  
Locally Compact

Weak spectral synthesis fails in the group algebra and the generalised group algebra of any non compact locally compact abelian group and also in the Fourier algebra of any infinite compact Lie group.

scholarly journals Multipliers for Amalgams and the Algebra S0(G)

1987 ◽  
Vol 39 (1) ◽  
pp. 123-148 ◽  
Author(s):  
Maria L. Torres De Squire
Keyword(s):  
Abelian Group ◽  
Haar Measure ◽  
Compact Abelian Group ◽  
Dual Group ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
The Difference ◽  
Image Position

Throughout the whole paper G will be a locally compact abelian group with Haar measure m and dual group Ĝ. The difference of two sets A and B will be denoted by A ∼ B, i.e.,For a function f on G and s ∊ G, the functions f′ and fs will be defined by

scholarly journals Multipliers on some weightedLp-spaces

2000 ◽  
Vol 23 (9) ◽  
pp. 651-656
Author(s):  
S. Öztop
Keyword(s):  
Abelian Group ◽  
Weight Function ◽  
Haar Measure ◽  
Compact Abelian Group ◽  
Locally Compact Abelian Group ◽  
Locally Compact

LetGbe a locally compact abelian group with Haar measuredx, and letωbe a symmetric Beurling weight function onG(Reiter, 1968). In this paper, using the relations betweenpiandqi, where1<pi,   qi<∞,pi≠qi(i=1,2), we show that the space of multipliers fromLωp(G)to the spaceS(q′1,q′2,ω−1), the space of multipliers fromLωp1(G)∩Lωp2(G)toLωq(G)and the space of multipliersLωp1(G)∩Lωp2(G)toS(q′1,q′2,ω−1).

Spans of translates in Lp(G)

1965 ◽  
Vol 5 (2) ◽  
pp. 216-233 ◽  
Author(s):  
R. E. Edwards
Keyword(s):  
Abelian Group ◽  
Haar Measure ◽  
Compact Abelian Group ◽  
Lebesgue Space ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Linear Combinations ◽  
Character Group ◽  
Weak Closure

Throughout this paper, G denotes a Hausdorff locally compact Abelian group, X its character group, and Lp(G) (1 ≦ p ≦ ∞) the usual Lebesgue space formed relative to the Haar measure on G. If f ∈ Lp(G), we denote by Tp[f] the closure (or weak closure, if p = ∞) in Lp(G) of the set linear combinations of translates of f.

Uniqueness of uniform norm and C*-norm in L p(G, ω)

2014 ◽  
Vol 64 (2) ◽  
Author(s):  
Ibrahim Akbarbaglu ◽  
Majid Heydarpour ◽  
Saeid Maghsoudi
Keyword(s):  
Abelian Group ◽  
Haar Measure ◽  
Compact Abelian Group ◽  
Uniform Norm ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Weighted Algebra

AbstractLet G be a locally compact abelian group with a fixed Haar measure and ω be a weight on G. For 1 < p < ∞, we study uniqueness of uniform and C*-norm properties of the invariant weighted algebra L p(G, ω).

A note on multipliers of Lp(G, A)

2003 ◽  
Vol 74 (1) ◽  
pp. 25-34 ◽  
Author(s):  
Serap Öztop
Keyword(s):  
Abelian Group ◽  
Banach Algebra ◽  
Compact Abelian Group ◽  
Commutative Banach Algebra ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Group 1

AbstractLet G be a locally compact abelian group, 1 < p < ∞, and A be a commutative Banach algebra. In this paper we study the space of multipliers on Lp (G, A) and characterize it as the space of multipliers of certain banach algebra. We also study the multipliers space on L1 (G, A) ∩ Lp (G, A).

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