scholarly journals Convolution algebras for topological groupoids with locally compact fibres

2011 ◽  
Vol 31 (2) ◽  
pp. 159
Author(s):  
Mădălina Roxana Buneci
Keyword(s):  
Locally Compact ◽  
Convolution Algebras ◽  
Topological Groupoids

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.

Multipliers of certain convolution algebras over locally compact semigroups

1980 ◽  
Vol 87 (1) ◽  
pp. 51-59 ◽  
Author(s):  
D. G. Todd
Keyword(s):  
Ordered Semigroup ◽  
Real Numbers ◽  
Locally Compact ◽  
Multiplier Algebra ◽  
Similar Work ◽  
Convolution Algebras ◽  
Compact Semigroups ◽  
Integrable Functions ◽  
Locally Compact Semigroups

In this paper we extend a result of Johnson and Lahr(3), which characterizes the multiplier algebra of L1(a, b) (the algebra of Lebesgue integrable functions on the interval of real numbers from a to b, under order convolution) to the L1 algebra of a general totally ordered semigroup. Similar work has been done in (l), but under more restrictive conditions.

scholarly journals Rigid cohomology of topological groupoids

1978 ◽  
Vol 26 (3) ◽  
pp. 277-301 ◽  
Author(s):  
K. A. MacKenzie
Keyword(s):  
Vector Bundles ◽  
Cohomology Theory ◽  
Unexpected Result ◽  
Vertex Group ◽  
Topological Groups ◽  
Locally Compact ◽  
Cohomology Space ◽  
Rigid Cohomology ◽  
Topological Groupoids

AbstractA cohomology theory for locally trivial, locally compact topological groupoids with coefficients in vector bundles is constructed, generalizing constructions of Hochschild and Mostow (1962) for topological groups and Higgins (1971) for discrete groupoids. It is calculated to be naturally isomorphic to the cohomology of the vertex groups, and is thus independent of the twistedness of the groupoid. The second cohomology space is accordingly realized as those “rigid” extensions which essentially arise from extensions of the vertex group; the cohomological machinery now yields the unexpected result that in fact all extensions, satisfying some natural weak conditions, are rigid.

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.

scholarly journals Imprimitivity theorem for groupoid representations

2011 ◽  
Vol 44 (1) ◽  
Author(s):  
Leszek Pysiak
Keyword(s):  
Group Representations ◽  
Locally Compact ◽  
Topological Groupoids

AbstractWe define and investigate the concept of the groupoid representation induced by a representation of the isotropy subgroupoid. Groupoids in question are locally compact transitive topological groupoids. We formulate and prove the imprimitivity theorem for such representations which is a generalization of the classical Mackey’s theorem known from the theory of group representations.

scholarly journals Amenability and Covariant Injectivity of Locally Compact Quantum Groups II

2017 ◽  
Vol 69 (5) ◽  
pp. 1064-1086 ◽  
Author(s):  
Jason Crann
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Locally Compact ◽  
Von Neumann ◽  
Relative Homology ◽  
Convolution Algebras ◽  
Locally Compact Quantum Groups ◽  
Locally Compact Quantum Group ◽  
Compact Quantum Groups ◽  
Group Von Neumann Algebra

AbstractBuilding on our previous work, we study the non-relative homology of quantum group convolution algebras. Our main result establishes the equivalence of amenability of a locally compact quantum group and 1-injectivity of as an operator -module. In particular, a locally compact group G is amenable if and only if its group von Neumann algebra VN(G) is 1-injective as an operator module over the Fourier algebra A(G). As an application, we provide a decomposability result for completely bounded -module maps on , and give a simpliûed proof that amenable discrete quantum groups have co-amenable compact duals, which avoids the use of modular theory and the Powers-Størmer inequality, suggesting that our homological techniques may yield a new approach to the open problem of duality between amenability and co-amenability.

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.

scholarly journals Morphisms which are continuous on a neighborhood of the base of a groupoid

2005 ◽  
Vol 42 (3) ◽  
pp. 265-276
Author(s):  
M. Buneci
Keyword(s):  
Negative Answer ◽  
Locally Compact ◽  
Topological Groupoids ◽  
Target Projection

Kirill Mackenzie raised in [3] (p. 31) the following question: given a morphism F : Ω → Ω′, where Ω and Ω′ are topological groupoids and F is continuous on a neighborhood of the base in Ω, is it true that is Ω continuous everywhere?This paper gives a negative answer to that question. Moreover, we shall prove that for a locally compact groupoid Ω with non-singleton orbits and having open target projection, if we assume that the continuity of every morphism F on a neighborhood of the base in Ω implies the continuity of F everywhere, then the groupoid Ω must be locally transitive.

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.

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