We construct a locally finite graph and a bounded geometry metric space which do not admit a quasi-isometric embedding into any uniformly convex Banach space. Connections with the geometry of c0 and superreflexivity are discussed. The question of coarse embeddability into uniformly convex Banach spaces became interesting after the recent work of G. Kasparov and G. Yu, who showed the coarse Novi...

in this paper, we investigate the concept of topological stationary for locally compact semigroups. in [4], t. mitchell proved that a semigroup s is right stationary if and only if m(s) has a left invariant mean. in this case, the set of values ?(f) where ? runs over all left invariant means on m(s) coincides with the set of constants in the weak* closed convex hull of right translates of f. th...

Recently, in [1], it has been proved that if B is an open unit ball in a Cartesian product l2 × l2 furnished with the lp-norm ‖ · ‖ and kB is the Kobayashi distance on B, then the metric space (B,kB) is locally uniformly convex in linear sense. Our construction of domains, which are locally uniformly convex in their Kobayashi distances, is based on the ideas from [1]. Such domains play an impor...