Vol. 56, No. 2, 1975

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Integral representations of weakly compact operators

A. Katsaras and Dar-Biau Liu

Vol. 56 (1975), No. 2, 547–556

Let X be a completely regular space and E,F locally convex spaces. Denote by Crc = Crc(X,E) the space of all continuous functions f from X into E for which f(X) is relatively compact. Uniformly continuous weakly compact operators from Crc into F are repreesented by integrals with respect to (E,F) valued measures on the algebra generated by the zero sets. Necessary and sufficient conditions for an operator to be continuous, with respect to certain topologies, are obtained. A sufficient condition for extending a measure to all Baire sets is given.

Mathematical Subject Classification 2000
Primary: 47B37
Received: 20 December 1973
Revised: 10 April 1974
Published: 1 February 1975
A. Katsaras
Dar-Biau Liu