Abstract
If E is a finitely generated Riesz subspace of C(X), where X is a compact Hausdorff space, containing the unit e, then Brown-Mertens- Ross have shown that the uniform closure of E is isomorphic to the uniform closure of the tensor product of the Riesz subspaces generated by s i , e (i = 1,…, m), where s 1, s 2,…, s m generate E. We extend their theorem to Archimedean f-algebras with unit and give applications to the theory of financial markets.
The authors thank C. D. Aliprantis, W. A. J. Luxemburg, and L. C. Moore, Jr. for their helpful comments and suggestions. Brown was supported in part by NSF grant SES 83-19611.
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© 1991 Springer-Verlag Berlin Heidelberg
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Brown, D.J., Huijsmans, C.B., de Pagter, B. (1991). Approximating Derivative Securities in f-Algebras. In: Positive Operators, Riesz Spaces, and Economics. Studies in Economic Theory, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58199-1_8
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DOI: https://doi.org/10.1007/978-3-642-58199-1_8
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