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A nonstandard proof of the Riesz representation theorem for weakly compact operators on C(Ω)

Published online by Cambridge University Press:  24 October 2008

Yeneng Sun
Yeneng Sun
Affiliation:
Department of Mathematics, University of Illinois, Urbana, Illinois 61801, U.S.A.
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Abstract

An easy way to construct the representing vector measures of weakly compact operators on C(Ω) is given by using the Loeb measure technique. This construction is not based on the Riesz representation theorem for linear functionals; thus we have a uniform way to treat the scalar and vector cases. Also the star finite representations of regular vector measures follow from the proof.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 1 , January 1989 , pp. 141 - 145
Copyright
Copyright © Cambridge Philosophical Society 1989

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