In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show that if $(e_alpha)_alpha$ is a bounded approximate identity modulo I of a Banach algebra A and X is a neo-unital modulo I, then $(e_alpha)_alpha$ is a bounded approximate identity for X. Moreover we show that amenability modulo an ideal of a Banach algebra A can be only considered ...

We show that for any abelian topological group G and arbitrary diffused submeasure μ, every continuous action of L0(μ,G) on a compact space has a fixed point. This generalizes earlier results of Herer and Christensen, Glasner, Furstenberg and Weiss, and Farah and Solecki. This also answers a question posed by Farah and Solecki. In particular, it implies that if H is of the form L0(μ,R), then H ...

We associate Popa systems (= standard invariants of subfactors, cf. [P3],[P4]) to the finite dimensional representations of compact quantum groups. We characterise the systems arising in this way: these are the ones which can be “represented” on finite dimensional Hilbert spaces. This is proved by an universal construction. We explicitely compute (in terms of some free products) the operation o...

We will discuss the motivating background leading to the consideration of the concept of amenability for von Neumann subfactors of nite Jones index and respectively for the combinatorial objects associated with them (standard graphs, standard lattices, paragroups, etc). Then we will review some of the results related to these notions of amenability, outlining the papers 20]{{25] and the lecture...

Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...