A uniform boundedness theorem for locally convex cones

Roth, Walter

doi:10.1090/S0002-9939-98-04699-1

A uniform boundedness theorem for locally convex cones
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Proc. Amer. Math. Soc. 126 (1998), 1973-1982 Request permission

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

Benno Fuchssteiner and Wolfgang Lusky, Convex cones, Notas de Matemática [Mathematical Notes], vol. 82, North-Holland Publishing Co., Amsterdam-New York, 1981. MR 640719
Klaus Keimel and Walter Roth, Ordered cones and approximation, Lecture Notes in Mathematics, vol. 1517, Springer-Verlag, Berlin, 1992. MR 1176514, DOI 10.1007/BFb0089190
A. P. Robertson and W. J. Robertson, Topological vector spaces, Cambridge Tracts in Mathematics and Mathematical Physics, No. 53, Cambridge University Press, New York, 1964. MR 0162118
Walter Roth, A combined approach to the fundamental theorems for normed spaces, Bull. Inst. Math. Acad. Sinica 22 (1994), no. 1, 83–89. MR 1280314
W. Roth, Hahn-Banach type theorems for locally convex cones, to appear.
Helmut H. Schaefer, Topological vector spaces, Graduate Texts in Mathematics, Vol. 3, Springer-Verlag, New York-Berlin, 1971. Third printing corrected. MR 0342978, DOI 10.1007/978-1-4684-9928-5