Charakterisierungen einiger Funktionenalgebren.
In this paper we define the notions of semicommutativity and semicommutativity modulo a linear subspace. We prove some results regarding the semicommutativity or semicommutativity modulo a linear subspace of a sequentially complete m-convex algebra. We show how such results can be applied in order to obtain commutativity criterions for locally m-convex algebras.
We consider the compactness of derivations from commutative Banach algebras into their dual modules. We show that if there are no compact derivations from a commutative Banach algebra, A, into its dual module, then there are no compact derivations from A into any symmetric A-bimodule; we also prove analogous results for weakly compact derivations and for bounded derivations of finite rank. We then characterise the compact derivations from the convolution algebra ℓ¹(ℤ₊) to its dual. Finally, we give...