Related papers: Can B(l^p) ever be amenable?

The seminal paper of Daubechies, Defrise, DeMol made clear that $\ell^p$ spaces with $p\in [1,2)$ and $p$-powers of the corresponding norms are appropriate settings for dealing with reconstruction of sparse solutions of ill-posed problems…

We study invariant pseudo-K\"ahler structures on a solvmanifold $G$ such that the Lie algebra $\mathfrak{g}$ is almost abelian, that is $\mathfrak{g}=\mathfrak{h}\rtimes\mathbb{R}$, with $\mathfrak{h}$ abelian; comparing with the…

We discuss the status of $b \to s \ell^+\ell^-$ decays in the post-$R_{K^{(*)}}$ era. The recent LHCb update of $R_K$ and $R_{K^*}$ measurements which are now compatible with the Standard Model, constrain new physics contributions to be…

Given Banach spaces E and F, we denote by ${\mathcal P}(^k!E,F)$ the space of all k-homogeneous (continuous) polynomials from E into F, and by ${\mathcal P}_{wb}(^k!E,F)$ the subspace of polynomials which are weak-to-norm continuous on…

The $L_p$-discrepancy is a quantitative measure for the irregularity of distribution of an $N$-element point set in the $d$-dimensional unit cube, which is closely related to the worst-case error of quasi-Monte Carlo algorithms for…

In view of both the latest LHCb measurement of $R_{K^{(*)}}$ and the new $2.8\sigma$ deviation reported by Belle II on $B^{+}\to K^{+}\nu\bar{\nu}$ decays, we present a fit to the $B$ meson anomalies for various one and two dimensional…

Complementing a recent observation of Newman and Rabinovich for $p=1$ we observe here that for all $0<p<2$ any $k$ points in $L_p$ embeds with distortion $(1+\e)$ into $\ell_p^n$ where $n$ is linear in $k$ (and polynomial in $\e^{-1}$).

Let $L^1_\om(G)$ be a Beurling algebra on a locally compact abelian group $G$. We look for general conditions on the weight which allows the vanishing of continuous derivations of $L^1_\om(G)$. This leads us to introducing vector-valued…

In this paper, we investigate the notion of approximate biprojectivity for semigroup algebras and for some Banach algebras related to semigroup algebras. We show that $\ell^{1}(S)$ is approximately biprojective if and only if $\ell^{1}(S)$…

We show that the tensor product of approximately amenable algebras need not be approximately amenable, and investigate conditions under which $A$ and $B$ being approximately amenable implies, or is implied by, $A\hat{\otimes}B$ or…

It is proved that a discrete group $G$ is amenable if and only if for every unitary representation of $G$ in an infinite-dimensional Hilbert space $\cal H$ the maximal uniform compactification of the unit sphere $\s_{\cal H}$ has a…

We show that for $1\leq p, q<\infty$ with $p/q \notin \mathbb{N}$, the doubly atomless separable $L_pL_q$ Banach lattice $L_p(L_q)$ is approximately ultrahomogeneous (AUH) over the class of its finitely generated sublattices. The above is…

In this paper, positive solutions to the Laplace equation with 1-dimensional circular singularities are investigated. First, we establish $L^p$ integrability estimates for such solutions $u$ near the singularities, in comparison with…

We study weak amenability of central Beurling algebras $ZL^1(G,\omega)$. The investigation is a natural extension of the known work on the commutative Beurling algebra $L^1(G,\omega)$. For [FC]$^-$ groups we establish a necessary condition…

It is shown that for every $p\in (2,\infty)$ there exists a doubling subset of $L_p$ that does not admit a bi-Lipschitz embedding into $\R^k$ for any $k\in \N$.

The notions of module pseudo-amenable and module pseudo-contractible Banach algebras are introduced. For a Banach algebra with bounded approximate identity, module pseudo-amenability and module approximate amenability are the same…

In this paper we study conditions on a Banach space X that ensure that the Banach algebra K(X) of compact operators is amenable. We give a symmetrized approximation property of X which is proved to be such a condition. This property is…

For a locally compact group $H$ with a left Haar measure, we study variable Lebesgue algebra $\mathcal{L}^{p(\cdot)}(H)$ with respect to a convolution. We show that if $\mathcal{L}^{p(\cdot)}(H)$ has bounded exponent, then it contains a…

Three natural definitions for amenability of general Hopf C^*-algebras (all of them being generalizations of the case of locally compact groups) were given and the relations between them were studied. Moreover, amenability in the situation…

We prove that amenability of a unitary co-representation $U$ of a locally compact quantum group passes to unitary co-representations that weakly contain $U$. This generalizes a result of Bekka, and answers affirmatively a question of…