Let G be a locally compact group, L p ( ) the usual ‐space for 1 ⩽ ∞, and A( Fourier algebra of . Our goal is to study, in new abstract context, completely bounded multipliers ), which we denote M cb ). We show that can characterised as ‘invariant part’ space (completely) normal ∞ )‐bimodule maps on B(L 2 )), operators In doing this develop function‐theoretic description X , μ)‐bimodule μ)), by V μ), name measurable Schur μ). approach leads many results, some generalise results hitherto...

Abstract We investigate generalized amenability and biflatness properties of various (operator) Segal algebras in both the group algebra, L 1 ( G ), Fourier A a locally compact .

We show that for any locally compact group $G$, the Fourier algebra $\mathrm {A}(G)$ is operator weakly amenable.

Let $G$ be a locally compact group. It is shown that there exists natural completely isometric representation of the bounded Fourier multiplier algebra $M_{cb}A(G)$, which dual to measure $M(G)$, on $\mathcal {B}(L_2(G))$. The image algebras $M(G)$ and $M_{cb}A(G)$ in {CB}^{\sigma } (\mathcal {B}(L_2(G)))$ are intrinsically characterized, some commutant theorems proved. also for any amenable group $G$, $UCB(\hat G)^*$ {B}(L_2(G))$, can regarded as duality result Neufang's theorem $LUC(G)^*$.

We study two related questions. (1) For a compact group $G$, what are the ranges of convolution maps on $\mathrm{A}(G\times G)$ given for $u,v$ in $\mathrm{A}(G)$ by $u\times v\mapsto u\ast\check{v}$ ($\check{v}(s)=v(s^{-1})$) and u

We investigate, for a locally compact group $G$, the operator amenability of Fourier–Stieltjes algebra $B(G)$ and reduced $B_r(G)$. The natural conjecture is that any these algebras amenable if only $G$ compact. partially prove this with mere replaced by $C$-amenability some constant $C\,{<}\, 5$. In process, we obtain new decomposition $B(G)$, which can be interpreted as non-commutative counterpart $M(G)$ into discrete continuous measures. further introduce variant – called...

Let G be a compact group and C(G) the C*-algebra of continuous complex-valued functions on G. The paper constructs an imbedding Fourier algebra A(G) into V(G) = C(G)⊗hC(G) (Haagerup tensor product) deduces results about parallel spectral synthesis, generalizing result Varopoulos. It then characterizes which diagonal sets in × are operator synthesis with respect to Haar measure, using definition due Arveson. This is applied obtain analogue Froelich: formula for algebras associated pre-orders...

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

We give for a compact group G, full characterization of when its Fourier algebra A(G) is weakly amenable: the connected component identity G e abelian. This condition also equivalent to hyper-Tauberian property A(G), and having anti-diagonal Δ = {(s,s -1 ): S ∈ G} be set spectral synthesis A(GxG). extend our results some classes non-compact, locally groups, including small invariant neighbourhood groups maximally almost periodic groups. close by illustrating curious relationship between...

Let $G$ be a locally compact group. It is not always the case that its reduced C*-algebra $C^*_r(G)$ admits tracial state. We exhibit closely related necessary and sufficient conditions for existence of such. gain complete answer when compactly generated. In particular almost connected, or more generally nuclear, trace equivalent to amenability. two examples classes totally disconnected groups which does admit

We study, for a locally compact group $G$, the compactifications $(\pi,G^\pi)$ associated with unitary representations $\pi$, which we call {\it $\pi$-Eberlein compactifications}. also study Gelfand spectra $\Phi_{\mathcal{A}}(\pi)}$ of uniformly closed algebras $\mathcal{A}(\pi)$ generated by matrix coefficients such $\pi$. note that $\Phi_{\mathcal{A}(\pi)}\cup\{0\}$ is itself semigroup and show Silov boundary $G^\pi$. containment relations various coefficients, give new characterisation...

Let $G$ be a locally compact group, $\mathrm{A}(G)$ its Fourier algebra and $\mathrm{L}^1(G)$ the space of Haar integrable functions on $G$. We study Segal ${\mathrm{S}^1\!\mathrm{A}(G)}= {\mathrm{A}(G)}\cap{\rm L}^1(G)$ in ${\mathrm{A}(G)}$.

Let<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"><mml:semantics><mml:mi>G</mml:mi><mml:annotation encoding="application/x-tex">G</mml:annotation></mml:semantics></mml:math></inline-formula>be a compact connected Lie group. The question of when weighted Fourier algebra on<inline-formula encoding="application/x-tex">G</mml:annotation></mml:semantics></mml:math></inline-formula>is completely isomorphic to an operator will...

Abstract Let G be a finitely generated group with polynomial growth, and let ω weight, i.e. sub-multiplicative function on positive values. We study when the weighted algebra ℓ 1 ( G, ) is isomorphic to an operator algebra. show that if weight large enough degree or exponential of order 0 &lt; α 1. demonstrate growth plays important role in this problem. Moreover, algebraic centre Q -algebra, hence satisfies multi-variable von Neumann inequality. also present more detailed our results...