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A uniform boundedness theorem for locally convex cones
Author(s):
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.
References:
- 1.
- B. Fuchssteiner and W. Lusky, Convex cones, vol. 56, North Holland Math. Studies, 1981. MR 83m:46018
- 2.
- K. Keimel, W. Roth, Ordered cones and approximation, Lecture Notes in Mathematics, vol. 1517, Springer Verlag, Heidelberg-Berlin-New York, 1992. MR 93i:46017
- 3.
- A.P. Robertson and W.J. Robertson, Topological vector spaces, Cambridge Tracts in Mathematics and Mathematical Physics, 1964. MR 28:5318
- 4.
- W. Roth, A combined approach to the Fundamental theorems for normed spaces, Bulletin Acad. Sinica 22 (1) (1994), 83-89. MR 95e:46019
- 5.
- W. Roth, Hahn-Banach type theorems for locally convex cones, to appear.
- 6.
- H.H. Schaefer, Topological vector spaces, Springer Verlag, Heidelberg-Berlin-New York, 1980. MR 49:7722 (1971 printing)
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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:
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
Copyright of article:
Copyright
1998,
American Mathematical Society
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