Vol. 20, No. 2, 1967

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A Hellinger integral representation for bounded linear functionals

James Ramsey Webb

Vol. 20 (1967), No. 2, 327–337

The function space considered is that consisting of the complex-valued, quasicontinuous functions on a real interval [aj,b], anchored at a, and having the LUB norm. It is shown that each bounded linear functional on this Banach space has a Hellinger integral representation. A formula for the norm of the functional is given in terms of the integrating functions involved in its representation. A new existence criterion for the Hellinger integral is uncovered on the way to the representation theorem.

Mathematical Subject Classification
Primary: 46.20
Received: 5 February 1966
Published: 1 February 1967
James Ramsey Webb