Factorization of operators mapping (F)-spaces into (DF)-spaces

Abstract

This paper deals with the factorization of linear operators mapping (F)-spaces into (DF)-spaces through Banach spaces and through operators of given operator ideals. Roughly speaking, we answer the question of, to what extend global properties of such operators are determined by their behaviour on the hounded subsets. The results are used to characterize the geometric structure of the neighbourhoods of zero in (F)-spaces by the geometry of their bounded sub-sets. Moreover, they allow further insights into the theory of nuclear (F)-spaces.