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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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  • 2. Klaus Keimel and Walter Roth, Ordered cones and approximation, Lecture Notes in Mathematics, vol. 1517, Springer-Verlag, Berlin, 1992. MR 1176514
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Additional Information

Walter Roth
Affiliation: Department of Mathematics, Universiti Brunei Darussalam, Bandar Seri Begawan 2028, Brunei Darussalam

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