derivations into n-th duals of ideals of banach algebras

Derivations Into N-th Duals of Ideals of Banach Algebras

Derivations into Duals of Closed Ideals of Banach Algebras

Let A be a Banach algebra. We study those closed ideals I of A for which the first cohomology group of A with coefficients in I is trivial; i.e. H(A, I) = {0}. We investigate such closed ideals when A is weakly amenable or biflat. Also we give some hereditary properties of ideal amenability.

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...

Derivations on Banach Algebras

The separating space of a derivation onA is a separating ideal [2, Chapter 5]; it also satisfies the same property for the left products. The following assertions are of the most famous conjectures about derivations on Banach algebras: (C1) every derivation on a Banach algebra has a nilpotent separating ideal; (C2) every derivation on a semiprime Banach algebra is continuous; (C3) every derivat...

Derivations of Commutative Banach Algebras

In [2] Singer and Wermer showed that a bounded derivation in a commutative Banach algebra 21 necessarily maps 21 into the radical 91. They conjectured at this time that the assumption of boundedness could be dropped. It is a corollary of results proved below that if 21 is in addition regular and semi-simple, this is indeed the case. What is actually proved here is that under the above hypothese...

σ-Derivations in Banach algebras