scholarly journals Biflatness and Pseudo-Amenability of Segal Algebras

2010 ◽  
Vol 62 (4) ◽  
pp. 845-869 ◽  
Author(s):  
Ebrahim Samei ◽  
Nico Spronk ◽  
Ross Stokke
Keyword(s):  
Compact Group ◽  
Group Algebra ◽  
Locally Compact Group ◽  
Fourier Algebra ◽  
Locally Compact ◽  
Segal Algebras

AbstractWe investigate generalized amenability and biflatness properties of various (operator) Segal algebras in both the group algebra, L1(G), and the Fourier algebra, A(G), of a locally compact group G.

scholarly journals Completely bounded bimodule maps and spectral synthesis

2017 ◽  
Vol 28 (10) ◽  
pp. 1750067 ◽  
Author(s):  
M. Alaghmandan ◽  
I. G. Todorov ◽  
L. Turowska
Keyword(s):  
Tensor Product ◽  
Compact Group ◽  
Closed Subset ◽  
Spectral Synthesis ◽  
Locally Compact Group ◽  
Product Formula ◽  
Fourier Algebra ◽  
Locally Compact ◽  
Multiplication Algebra

We initiate the study of the completely bounded multipliers of the Haagerup tensor product [Formula: see text] of two copies of the Fourier algebra [Formula: see text] of a locally compact group [Formula: see text]. If [Formula: see text] is a closed subset of [Formula: see text] we let [Formula: see text] and show that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] then [Formula: see text] is a set of local spectral synthesis for [Formula: see text]. Conversely, we prove that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] and [Formula: see text] is a Moore group then [Formula: see text] is a set of spectral synthesis for [Formula: see text]. Using the natural identification of the space of all completely bounded weak* continuous [Formula: see text]-bimodule maps with the dual of [Formula: see text], we show that, in the case [Formula: see text] is weakly amenable, such a map leaves the multiplication algebra of [Formula: see text] invariant if and only if its support is contained in the antidiagonal of [Formula: see text].

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.

scholarly journals Operator Amenability of the Fourier Algebra in the cb-Multiplier Norm

2007 ◽  
Vol 59 (5) ◽  
pp. 966-980 ◽  
Author(s):  
Brian E. Forrest ◽  
Volker Runde ◽  
Nico Spronk
Keyword(s):  
Compact Group ◽  
Free Group ◽  
Discrete Group ◽  
Amenable Group ◽  
Locally Compact Group ◽  
Approximate Identity ◽  
Fourier Algebra ◽  
Locally Compact ◽  
Residually Finite ◽  
Finite Dimensional

AbstractLet G be a locally compact group, and let Acb(G) denote the closure of A(G), the Fourier algebra of G, in the space of completely boundedmultipliers of A(G). If G is a weakly amenable, discrete group such that C*(G) is residually finite-dimensional, we show that Acb(G) is operator amenable. In particular, Acb() is operator amenable even though , the free group in two generators, is not an amenable group. Moreover, we show that if G is a discrete group such that Acb(G) is operator amenable, a closed ideal of A(G) is weakly completely complemented in A(G) if and only if it has an approximate identity bounded in the cb-multiplier norm.

Unit Elements in the Double Dual of a Subalgebra of the Fourier Algebra A(G)

2009 ◽  
Vol 61 (2) ◽  
pp. 382-394
Author(s):  
Tianxuan Miao
Keyword(s):  
Compact Group ◽  
Banach Algebra ◽  
Locally Compact Group ◽  
Approximate Identity ◽  
Fourier Algebra ◽  
Locally Compact ◽  
Arens Product ◽  
The Right ◽  
Topological Centers ◽  
The Relationship

Abstract. Let 𝒜 be a Banach algebra with a bounded right approximate identity and let ℬ be a closed ideal of 𝒜. We study the relationship between the right identities of the double duals ℬ** and 𝒜** under the Arens product. We show that every right identity of ℬ** can be extended to a right identity of 𝒜** in some sense. As a consequence, we answer a question of Lau and Ülger, showing that for the Fourier algebra A(G) of a locally compact group G, an element ϕ ∈ A(G)** is in A(G) if and only if A(G)ϕ ⊆ A(G) and Eϕ = ϕ for all right identities E of A(G)**. We also prove some results about the topological centers of ℬ** and 𝒜**.

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.

On $${\phi}$$ -contractibility of the Lebesgue–Fourier algebra of a locally compact group

2010 ◽  
Vol 95 (4) ◽  
pp. 373-379 ◽  
Author(s):  
Mahmood Alaghmandan ◽  
Rasoul Nasr-Isfahani ◽  
Mehdi Nemati
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Fourier Algebra ◽  
Locally Compact

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).

Invariant Means on a Class of von Neumann Algebras Related to Ultraspherical Hypergroups II

2017 ◽  
Vol 60 (2) ◽  
pp. 402-410
Author(s):  
N. Shravan Kumar
Keyword(s):  
Compact Group ◽  
Von Neumann Algebras ◽  
Locally Compact Group ◽  
Fourier Algebra ◽  
Locally Compact ◽  
Von Neumann ◽  
Invariant Means

AbstractLet K be an ultraspherical hypergroup associated with a locally compact group G and a spherical projector π and let VN(K) denote the dual of the Fourier algebra A(K) corresponding to K. In this note, we show that the set of invariant means on VN(K) is singleton if and only if K is discrete. Here K need not be second countable. We also study invariant means on the dual of the Fourier algebra A0(K), the closure of A(K) in the cb-multiplier norm. Finally, we consider generalized translations and generalized invariant means.

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