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...

We survey the recent investigations on (bounded, sequential) approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We will discuss the core problems concerning these notions and address the signicance of any solutions to them to the development of the eld.

The effect of elevated CO(2) and O(3) on apparent quantum yield (varphi), maximum photosynthesis (P(max)), carboxylation efficiency (V(cmax)) and electron transport capacity (J(max)) at different canopy locations was studied in two aspen (Populus tremuloides) clones of contrasting O(3) tolerance. Local light climate at every leaf was characterized as fraction of above-canopy photosynthetic phot...

Regularity properties significantly stronger than were previously known are developed for four-dimensional non-linear conformally invariant quantized fields. The Fourier coefficients of the interaction Lagrangian in the interaction representation-i.e., evaluated after substitution of the associated quantized free field-is a densely defined operator on the associated free field Hilbert space K. ...

We investigate the spatiotemporal coding of low amplitude inputs to a simple system of globally coupled phase oscillators with coupling function g(varphi)=-sin(varphi+alpha)+rsin(2varphi+beta) that has robust heteroclinic cycles (slow switching between cluster states). The inputs correspond to detuning of the oscillators. It was recently noted that globally coupled phase oscillators can encode ...