This is a study of (spaces of)
[weakly] compact linear operators with ranges in Fréchet 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.
