�ber einen Homomorphiesatz von G.K�the

Abstract

The main object of this paper is to generalize a homomorphism theorem of Kothe [5] for a wide class of not necessarily locally convex topological vector spaces. A sequence σ=(Bn) of balanced sets Bn in a vector space E(τ), such that the union of the Bn's equals E and such that Bn+Bn⊂Bn+1 for all n∈N, is called an absorbent sequence. E(τ) is called σ-locally topological, if it possesses an absorbent sequence σ=(Bn) of bounded sets and if a linear mapping A from E(τ) into any other vector space is continuous if all restrictions\(A|_{B_n }\) are continuous at 0. It is shown, that a continuous linear mapping A from a vector space E(τ) with an absorbant sequence of compact sets into a boundedly summing σ-locally topological space F(τ′) is a homomorphism if A(E) is closed in F(τ′).