Vol. 35, No. 2, 1970

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A v-integral representation for linear operators on spaces of continuous functions with values in topological vector spaces

John R. Edwards and Stanley G. Wayment

Vol. 35 (1970), No. 2, 327–330

Suppose X and Y are topological vector spaces. This paper gives an analytic representation of continuous linear operators from C into Y , where C denotes the space of continuous functions from the interval [0,1] into X with the topology of uniform convergence. In order to obtain an integral representation theorem analogous to the ones given by R. K. Goodrich for the locally convex setting in Trans. Amer. Math. Soc. 131 (1968), 246-258, certain strong hypotheses on C must be assumed because of the need to be able to extend the operators to a subset of the double dual of C. However, by using the notion of v-integral, it is possible to avoid this problem and give a representation theorem without additional hypothesis.

Mathematical Subject Classification
Primary: 28.50
Secondary: 47.00
Received: 5 January 1970
Published: 1 November 1970
John R. Edwards
Stanley G. Wayment