On reducibility of some operator semigroups and algebras on locally convex spaces.
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.
A new, unified presentation of the ideal norms of factorization of operators through Banach lattices and related ideal norms is given.
In a previous paper we gave an example of a finite distributive subspace lattice ℒ on a Hilbert space and a rank two operator of Algℒ that cannot be written as a finite sum of rank one operators from Algℒ. The lattice ℒ was a specific realization of the free distributive lattice on three generators. In the present paper, which is a sequel to the aforementioned one, we study Algℒ for the general free distributive lattice with three generators (on a normed space). Necessary and sufficient conditions...