For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. We give some examples of completely continuous Banach algebras and a suffici...

We introduce a notion of amenable normal extension S unital ring R with finite approximation system F, encompassing the algebras over field Gromov and Elek, twisted crossed product by an group, tensor extension. It is shown that every Sylvester matrix rank function rk preserved has canonical to rk_F for S. In case extension, it also depends on continuously. When group action C*-algebra preservi...

Abstract It is shown that each locally compact second countable non-(T) group G admits non-strongly ergodic weakly mixing IDPFT Poisson actions of any possible Krieger type. These are amenable if and only amenable. If has the Haagerup property, then (and then) these can be chosen 0-type. amenable, Bernoulli arbitrary