Let A and B be simple separable nuclear monotracial C⁎-algebras, let α β strongly outer actions of a countable discrete amenable group Γ on B, respectively. In this paper, we show that α⊗idW A⊗W β⊗idW B⊗W are cocycle conjugate where W is the Razak-Jacelon algebra. Also, characterize such by using fixed point subalgebras Kirchberg's central sequence C⁎-algebras.

Let (μn : n ≥ 0) be Borel probabilities on a metric space S such that μn → μ0 weakly. Say that Skorohod representation holds if, on some probability space, there are S-valued random variables Xn satisfying Xn ∼ μn for all n and Xn → X0 in probability. By Skorohod’s theorem, Skorohod representation holds (with Xn → X0 almost uniformly) if μ0 is separable. Two results are proved in this paper. Fi...

We prove that for every homogeneous and strongly locally homogeneous separable metrizable space X there is a metrizable compactification γX of X such that, among other things, for all x, y ∈ X there is a homeomorphism f : γX → γX such that f(x) = y. This implies that X is a coset space of some separable metrizable topological group G.

In this paper we study linear into isometries of non-reflexive spaces (embeddings) that preserve finite dimensional structure of the range space. We consider this for various aspects of the finite dimensional structure, covering the recent notion of an almost isometric ideals introduced by Abrahamsen et.al., the well studied notions of a M -ideal and that of an ideal. We show that if a separabl...