Related papers: Amenable cones are particularly nice
Inner amenability is a bridge between amenability of an object and amenability of its operator algebras. It is an open problem of Ananantharman-Delaroche to decide whether all \'etale groupoids are inner amenable. Approximate lattices and…
Tensor products of convex cones have recently come up in different areas, ranging from functional analysis and operator theory to approximation theory and theoretical physics. However, most of the existing literature focuses either on…
This note conducts a comparative study of some approximating properties of the metric projection, generalized projection, and generalized metric projection in uniformly convex and uniformly smooth Banach spaces. We prove that the inverse…
In this paper we consider a partial overdetermined mixed boundary value problem in domains inside a cone as in [18]. We show that in cones having an isoperimetric property the only domains which admit a solution and which minimize a…
A new line of research on the lasso exploits the beautiful geometric fact that the lasso fit is the residual from projecting the response vector $y$ onto a certain convex polytope. This geometric picture also allows an exact geometric…
Recent research in coarse geometry revealed similarities between certain concepts of analysis, large scale geometry, and topology. Property A of G.Yu is the coarse analog of amenability for groups and its generalization (exact spaces) was…
The conic structure of the convex cone of non-negative operator convex functions on $(0,\infty)$ (also on $(-1,1)$) is clarified. We completely determine the extreme rays, the closed faces, and the simplicial closed faces of this convex…
Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the…
Making use of a simplified model for protein folding, it can be shown that conformations which are particularly stable when their energy is minimized with respect to amino acid sequence (in the sense that they display a large energy gap to…
In this article we analyze the notions of amenability and paradoxical decomposition from an algebraic perspective. We consider this dichotomy for locally finite extended metric spaces and for general algebras over commutative fields. In the…
We introduce the notions of approximate Connes-amenability and approximate strong Connes-amenability for dual Banach algebras. Then we characterize these two types of algebras in terms of approximate normal virtual diagonals and approximate…
We present a study of cubic surfaces from the novel perspective of positive geometry. Our positive geometries have dimension two (the surface minus its 27 lines), dimension three (its complement in 3-space), and dimension four (the moduli…
We study the connection between amenability, F{\o}lner conditions and the geometry of finitely generated semigroups. Using results of Klawe, we show that within an extremely broad class of semigroups (encompassing all groups, left…
While faces of a polytope form a well structured lattice, in which faces of each possible dimension are present, this is not true for general compact convex sets. We address the question of what dimensional patterns are possible for the…
An alternative, geometrical proof of a known theorem concerning the decomposition of positive maps of the matrix algebra $M_{2}(\mathbb{C})$ has been presented. The premise of the proof is the identification of positive maps with operators…
We prove that the following are equivalent for a locally compact group $G$: (i) $G$ is amenable; (ii) $M(G)$ is Connes-amenable; (iii) $M(G)$ has a normal, virtual diagonal.
We study stability properties of amenable locally compact quantum groups under the bicrossed product construction. We obtain as our main result an equivalence between amenability of the bicrossed product and amenability of the matched…
We define a Banach algebra A to be dual if $A = (A_\ast)^\ast$ for a closed submodule $A_\ast$ of $A^\ast$. The class of dual Banach algebras includes all $W^\ast$-algebras, but also all algebras M(G) for locally compact groups G, all…
We study amenability of affine algebras (based on the notion of almost-invariant finite-dimensional subspace), and apply it to algebras associated with finitely generated groups. We show that a group G is amenable if and only if its group…
We investigate asymptotically flat manifolds with cone structure at infinity. We show that any such manifold M has a finite number of ends. For simply connected ends we classify all possible cones at infinity, except for the 4-dimensional…