Vol. 98, No. 2, 1982

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[Weakly] compact operators and DF spaces

Wolfgang Ruess

Vol. 98 (1982), No. 2, 419–441

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.

Mathematical Subject Classification
Primary: 47D30, 47D30
Received: 14 March 1980
Revised: 11 November 1980
Published: 1 February 1982
Wolfgang Ruess