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Separation and Approximation in Topological Vector Lattices

Published online by Cambridge University Press:  20 November 2018

Solomon Leader
Solomon Leader*
Affiliation:
Rutgers University
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Spectral theory in its lattice-theoretic setting proves abstractly that the indicators of measurable sets generate the space L of Lebesgue-integrable functions on an interval. We are concerned here with abstractions suggested by the fact that indicators of intervals suffice to generate L. Our results show that the approximation of arbitrary elements of a topological vector lattice rests upon the ability to separate disjoint elements/ and g by an operation that behaves in the limit like a projection annihilating/ and leaving g invariant.

The introduction of this concept of separation together with the notion of limit unit leads (via the Fundamental Lemma) to abstract generalizations of the Radon-Nikodym Theorem (Theorem 1) and the Stone-Weierstrass Theorem (Theorem 3).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 11 , 1959 , pp. 286 - 296
Copyright
Copyright © Canadian Mathematical Society 1959

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