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A type of nearest point set in a complete $ l$-group

Author: Michael Keisler
Journal: Proc. Amer. Math. Soc. 67 (1977), 189-197
MSC: Primary 06A55
MathSciNet review: 0463071
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Abstract: A theorem by W. D. L. Appling (Riv. Mat. Univ. Parma, (3) 2 (1973), 251-276) demonstrates that a C-set is a nearest point set in $ {\text{ba}}(S,\Sigma )$ with respect to the variation norm. This paper demonstrates an analogous result for a generalized form of C-set in a complete l-group with distance with respect to the norm being replaced by a stronger property definable in a complete l-group (distance between elements x and y of a complete l-group G is taken to be $ \vert x - y\vert$). The result is then shown to be a characterization of sets possessing the stronger property in the case of a complete vector lattice, but not a characterization in the case of a complete l-group.

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Keywords: Complete l-group, complete vector lattice, complex, l-nearest point set, normal subgroup, projection operator
Article copyright: © Copyright 1977 American Mathematical Society

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