[Weakly] compact operators and DF spaces

Abstract

This is a study of (spaces of) [weakly] compact linear operators with ranges in Frchet spaces. Characterizations of such operators, extensions and refinements of Schauder's and Gantmaher's Theorems, and results on the approximation property of the space K{X, Y) of compact linear operators are given, together with applications to [weakly] compact operators on function spaces with the strict topology of R. C. Buck. Finally, a new tensor product representation for K*(X, Y), X and Y Banach, is established, and compact sets of compact operators on Banach spaces are characterized. The main tools are extensions of Grothendieck's DF techniques.