On the radical in Hermitian LMC algebras
In this paper we prove that the image of a nth order derivation on real commutative Banach ℓ-algebras with positive squares is contained in the set of nilpotent elements.
We describe an ultrametric version of the Stone-Weierstrass theorem, without any assumption on the residue field. If is a subset of a rank-one valuation domain , we show that the ring of polynomial functions is dense in the ring of continuous functions from to if and only if the topological closure of in the completion of is compact. We then show how to expand continuous functions in sums of polynomials.
We investigate the weak amenability of the Banach algebra ℬ(X) of all bounded linear operators on a Banach space X. Sufficient conditions are given for weak amenability of this and other Banach operator algebras with bounded one-sided approximate identities.