scholarly journals ON HOMOLOGICAL PROPERTIES FOR SOME MODULES OF UNIFORMLY CONTINUOUS FUNCTIONS OVER CONVOLUTION ALGEBRAS

2011 ◽  
Vol 84 (2) ◽  
pp. 177-185
Author(s):  
RASOUL NASR-ISFAHANI ◽  
SIMA SOLTANI RENANI
Keyword(s):  
Compact Group ◽  
Group Algebra ◽  
Dual Space ◽  
Continuous Functions ◽  
Locally Compact Group ◽  
Measure Algebra ◽  
Locally Compact ◽  
Convolution Algebras ◽  
Uniformly Continuous

AbstractFor a locally compact group G, let LUC(G) denote the space of all left uniformly continuous functions on G. Here, we investigate projectivity, injectivity and flatness of LUC(G) and its dual space LUC(G)* as Banach left modules over the group algebra as well as the measure algebra of G.

Compactifications of locally compact groups and quotients

1994 ◽  
Vol 116 (3) ◽  
pp. 451-463 ◽  
Author(s):  
A. T. Lau ◽  
P. Milnes ◽  
J. S. Pym
Keyword(s):  
Normal Subgroup ◽  
Compact Group ◽  
Semidirect Product ◽  
Continuous Functions ◽  
Locally Compact Group ◽  
Positive Answer ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Uniformly Continuous

AbstractLet N be a compact normal subgroup of a locally compact group G. One of our goals here is to determine when and how a given compactification Y of G/N can be realized as a quotient of the analogous compactification (ψ, X) of G by Nψ = ψ(N) ⊂ X; this is achieved in a number of cases for which we can establish that μNψ ⊂ Nψ μ for all μ ∈ X A question arises naturally, ‘Can the latter containment be proper?’ With an example, we give a positive answer to this question.The group G is an extension of N by GN and can be identified algebraically with Nx GN when this product is given the Schreier multiplication, and for our further results we assume that we can also identify G topologically with N x GN. When GN is discrete and X is the compactification of G coming from the left uniformly continuous functions, we are able to show that X is an extension of N by (GN)(X≅N x (G/N)) even when G is not a semidirect product. Examples are given to illustrate the theory, and also to show its limitations.

Bipositive and Isometric Isomorphisms of Some Convolution Algebras

1965 ◽  
Vol 17 ◽  
pp. 839-846 ◽  
Author(s):  
R. E. Edwards
Keyword(s):  
Compact Group ◽  
Lebesgue Space ◽  
Inductive Limit ◽  
Continuous Functions ◽  
Locally Compact Group ◽  
Natural Topology ◽  
Locally Compact ◽  
Convolution Algebras ◽  
Image Position ◽  
Complex Valued

Throughout this paper the term "space" will mean "Hausdorff locally compact space" and the term '"group" will mean "Hausdorff locally compact group." If G is a group and 1 ≤ p < ∞, Lp(G) denotes the usual Lebesgue space formed relative to left Haar measure on G. It is well known that L1(G) is an algebra under convolution, and that the same is true of Lp(G) whenever G is compact. We introduce also the space Cc(G) of complex-valued continuous functions f on G for each of which the support (supp f), is compact. The "natural" topology of CC(G) is obtained by regarding CC(G) as the inductive limit of its subspaces

Uniformly Continuous Functionals and M-Weakly Amenable Groups

2013 ◽  
Vol 65 (5) ◽  
pp. 1005-1019 ◽  
Author(s):  
Brian Forrest ◽  
Tianxuan Miao
Keyword(s):  
Compact Group ◽  
Amenable Group ◽  
Locally Compact Group ◽  
Approximate Identity ◽  
Fourier Algebra ◽  
Locally Compact ◽  
Amenable Groups ◽  
Invariant Means ◽  
Continuous Functionals ◽  
Uniformly Continuous

AbstractLet G be a locally compact group. Let AM(G) (A0(G))denote the closure of A(G), the Fourier algebra of G in the space of bounded (completely bounded) multipliers of A(G). We call a locally compact group M-weakly amenable if AM(G) has a bounded approximate identity. We will show that when G is M-weakly amenable, the algebras AM(G) and A0(G) have properties that are characteristic of the Fourier algebra of an amenable group. Along the way we show that the sets of topologically invariant means associated with these algebras have the same cardinality as those of the Fourier algebra.

On the Extension of Uniformly Continuous Functions(1)

1975 ◽  
Vol 18 (1) ◽  
pp. 143-145 ◽  
Author(s):  
L. T. Gardner ◽  
P. Milnes
Keyword(s):  
Continuous Function ◽  
Uniform Space ◽  
Continuous Extension ◽  
Continuous Functions ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Totally Bounded ◽  
Special Cases ◽  
Uniformly Continuous Function ◽  
Uniformly Continuous

AbstractA theorem of M. Katětov asserts that a bounded uniformly continuous function f on a subspace Q of a uniform space P has a bounded uniformly continuous extension to all of P. In this note we give new proofs of two special cases of this theorem: (i) Q is totally bounded, and (ii) P is a locally compact group and Q is a subgroup, both P and Q having the left uniformity.

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 Non commutative convolution measure algebras with no proper L-ideals

1989 ◽  
Vol 40 (1) ◽  
pp. 13-23 ◽  
Author(s):  
Sahl Fadul Albar
Keyword(s):  
Compact Group ◽  
Group Algebra ◽  
Locally Compact Group ◽  
Dimensional Representation ◽  
Locally Compact ◽  
Finite Dimensional Representation ◽  
Finite Dimensional

We study non-commutative convolution measure algebras satisfying the condition in the title and having an involution with a non-degenerate finite dimensional *-representation. We show first that the group algebra L1(G) of a locally compact group G satisfies these conditions. Then we show that to a given algebra A with the above conditions there corresponds a locally compact group G such that A is a * and L-subalgebra of M(G) and such that the enveloping C*-algebra of A is *isomorphic to C*(G). Finally we show for certain groups that L1(G) is the only example of such algebras, thus giving a characterisation of L1(G).

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.

Sign in / Sign up

Export Citation Format

Share Document