Ultrapowers of Banach Algebras

Amenability of ultrapowers of Banach algebras

We study when certain properties of Banach algebras are stable under ultrapower constructions. In particular, we consider when every ultrapower of A is Arens regular, and give some evidence that this is so if and only if A is isomorphic to a closed subalgebra of operators on a super-reflexive Banach space. We show that such ideas are closely related to whether one can sensibly define an ultrapo...

Ultrapowers of Banach algebras and modules

The Arens products are the standard way of extending the product from a Banach algebra A to its bidual A′′. Ultrapowers provide another method which is more symmetric, but one that in general will only give a bilinear map, which may not be associative. We show that if A is Arens regular, then there is at least one way to use an ultrapower to recover the Arens product, a result previously known ...

amenability of banach algebras

chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...

varphi-amenability of Banach algebras

Let $A$ be an arbitrary Banach algebra and $varphi$ a homomorphism from $A$ onto $Bbb C$. Our first purpose in this paper is to give some equivalent conditions under which guarantees a $varphi$-mean of norm one. Then we find some conditions under which there exists a $varphi$-mean in the weak$^*$ cluster of ${ain A; |a|=varphi(a)=1}$ in $A^{**}$.

Biflatness and Biprojectivitiy of Triangular Banach Algebras