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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
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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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