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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A uniform boundedness theorem
for locally convex cones


Author: Walter Roth
Journal: Proc. Amer. Math. Soc. 126 (1998), 1973-1982
MSC (1991): Primary 46A08, 46A30
MathSciNet review: 1476390
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Abstract: We prove a uniform boundedness theorem for families of linear operators on ordered cones. Using the concept of locally convex cones we introduce the notions of barreled cones and of weak cone-completeness. Our main result, though no straightforward generalization of the classical case, implies the Uniform Boundedness Theorem for Fréchet spaces.


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Additional Information

Walter Roth
Affiliation: Department of Mathematics, Universiti Brunei Darussalam, Bandar Seri Begawan 2028, Brunei Darussalam
Email: roth@ubd.edu.bn

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04699-1
PII: S 0002-9939(98)04699-1
Keywords: Uniform boundedness theorem, locally convex cones
Received by editor(s): July 15, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society