Abstract Amenability is a notion of facial exposedness for convex cones that stronger than being facially dual complete (or ‘nice’) which is, in turn, merely exposed. Hyperbolicity are family algebraically structured closed contain all spectrahedral (linear sections positive semidefinite cones) as special cases. It known amenable. We establish hyperbolicity As part the argument, we show any fac...

Amenable category is a variant of the Lusternik-Schnirelman category, based on covers by amenable open subsets. We study monotonicity problem for degree-one maps and relation between topological complexity.

Let S be a semigroup with a left multiplier  on S. A new product on S is defined by  related to S and  such that S and the new semigroup ST have the same underlying set as S. It is shown that if  is injective then where, is the extension of  on  Also, we show that if  is bijective then is amenable if and only if is so. Moreover, if  S completely regular, then is weakly amenable. 

This is a detailed survey on the QWEP conjecture and Connes’ embedding problem. Most of contents are taken from Kirchberg’s paper [Invent. Math. 112 (1993)].

In this paper, we verify the $L^p$ coarse Baum–Connes conjecture for spaces with finite asymptotic dimension $p\in\[1,\infty)$. We also show that $K$-theory of Roe algebras is independent $p\in(1,\infty)$ dimension.