Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-98-04699-1
MathSciNet review: 1476390
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46A08, 46A30

Retrieve articles in all journals with MSC (1991): 46A08, 46A30


Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-98-04699-1
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

American Mathematical Society