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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Continuous lattice ordering by Schauder basis cones


Author: John T. Hofler
Journal: Proc. Amer. Math. Soc. 30 (1971), 527-532
MSC: Primary 46A40
MathSciNet review: 0415264
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Abstract: Let (E, $ \tau $) be a barrelled Hausdorff space lattice ordered by the cone of an unconditional Schauder basis $ ({x_n},{f_n})$. It is shown that under such an ordering (E, T) is a locally convex lattice. Necessary and sufficient conditions are given for the lattice operations to be continuous with respect to the weak topologies on E and its topological dual $ E'$: the lattice operations are $ \sigma (E,E')$-continuous on E if and only if $ \{ {f_n}:n \in \omega \} $ is a Hamel basis for $ E'$.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0415264-X
Keywords: Continuous lattice operations, Schauder basis cones, unconditional Schauder basis
Article copyright: © Copyright 1971 American Mathematical Society