Related papers: Rigidity results for $L^p$-operator algebras and a…

Let $L_{A}=-{\rm div}(A\nabla)$ be an elliptic divergence form operator with bounded complex coefficients subject to mixed boundary conditions on an arbitrary open set $\Omega\subseteq\mathbb{R}^{d}$. We prove that the maximal operator…

Given a complex, elliptic coefficient function we investigate for which values of $p$ the corresponding second-order divergence form operator, complemented with Dirichlet, Neumann or mixed boundary conditions, generates a strongly…

We show that the following operator algebras have hyperarithmetic theory: the hyperfinite II$_1$ factor $\mathcal R$, $L(\Gamma)$ for $\Gamma$ a finitely generated group with solvable word problem, $C^*(\Gamma)$ for $\Gamma$ a finitely…

The notion of rigidity of Lie algebra is linked to the following problem: when does a Lie brackets $\mu$ on a vector space g satisfy that every Lie bracket $\mu_1$ sufficiently close to $\mu$ is of the form $\mu_1 = P.\mu $ for some P in…

For a nontrivial locally compact group $G$, and $p\in [1,\infty)$, consider the Banach algebras of $p$-pseudofunctions, $p$-pseudomeasures, $p$-convolvers, and the full group $L^p$-operator algebra. We show that these Banach algebras are…

For $n\geq 3,$ let $\Gamma=SL_n(\mathbb Z).$ We prove the following superridigity result for $\Gamma$ in the context of operator algebras. Let $L(\Gamma)$ be the von Neumann algebra generated by the left regular representation of $\Gamma.$…

We construct discrete groups $G$ with infinite center that are nevertheless W*-superrigid, meaning that the group von Neumann algebra $L(G)$ fully remembers the group $G$. We obtain these rigidity results both up to isomorphisms and up to…

Let $L$ denote a right-invariant sub-Laplacian on an exponential, hence solvable Lie group $G$, endowed with a left-invariant Haar measure. Depending on the structure of $G$, and possibly also that of $L$, $L$ may admit differentiable…

Given a domain above a Lipschitz graph, we establish solvability results for strongly elliptic second-order systems in divergence-form, allowed to have lower-order (drift) terms, with $L^p$-boundary data for $p$ near $2$ (more precisely, in…

We show that a Hausdorff, ample groupoid $\mathcal{G}$ can be completely recovered from the $I$-norm completion of $C_c(\mathcal{G})$. More generally, we show that this is also the case for the algebra of symmetrized $p$-pseudofunctions, as…

Let $G$ be a locally compact group and $\omega$ be a continuous weight on $G$. In this paper, we first characterize bicontinuous biseparating algebra isomorphisms between weighted $L^p$-algebras. As a result we extend previous results of…

We prove that the realization $A_p$ in $L^p(\mathbb{R}^N),\,1<p<\infty$, of the elliptic operator $A=(1+|x|^{\alpha})\Delta+b|x|^{\alpha-1}\frac{x}{|x|}\cdot \nabla-c|x|^{\beta}$ with domain $D(A_p) =\{ u \in W^{2,p}(\mathbb{R}^N)\, |\, Au…

This article contains two rigidity type results for $\mathrm{SL}(n,\mathbb{Z})$ for large $n$ that share the same proof. Firstly, we prove that for every $p \in [1,\infty]$ different from $2$, the noncommutative $L^p$-space associated with…

We introduce the notion of (strong) subexponential growth for \'etale groupoids and study its basic properties. In particular, we show that the K-groups of the associated groupoid $L^p$-operator algebras are independent of $p \in…

We define spatial $L^p$ AF algebras for $p \in [1, \infty) \setminus \{ 2 \}$, and prove the following analog of the Elliott AF algebra classification theorem. If $A$ and $B$ are spatial $L^p$ AF algebras, then the following are equivalent:…

For $1<p<\infty$, we prove (i) a version of Voiculescu's absorption theorem for operators on $l^{p}$, (ii) that $\mathrm{Ext}_{\sim,s}(\mathcal{A},K(l^{p}))$ is a group for certain Banach algebra $\mathcal{A}$, and (iii) homotopy invariance…

A group $G$ is called $W^*$-superrigid (resp. $C^*$-superrigid) if it is completely recognizable from its von Neumann algebra $L(G)$ (resp. reduced $C^*$-algebra $C_r^*(G)$). Developing new technical aspects in Popa's deformation/rigidity…

It is well-known that Littlewood-Paley operators formed with respect to lacunary sets of finite order are bounded on $L^p (\mathbb{R})$ for all $1<p<\infty$. In this note it is shown that $$ \| S_{\mathcal{I}_{E_2}} \|_{L^p (\mathbb{R})…

We show weighted non-autonomous $L^q(L^p)$ maximal regularity for families of complex second-order systems in divergence form under a mixed regularity condition in space and time. To be more precise, we let $p,q \in (1,\infty)$ and we…

We present a unified and concise method for establishing L^p Hardy and Rellich inequalities for a broad class of subelliptic operators of divergence type. The approach, based on a fundamental algebraic identity, provides explicit control on…