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)

 
 

 

Extending continuous linear functionals in convergence inductive limit spaces


Authors: S. K. Kranzler and T. S. McDermott
Journal: Proc. Amer. Math. Soc. 43 (1974), 357-360
MSC: Primary 46A05
DOI: https://doi.org/10.1090/S0002-9939-1974-0333639-7
MathSciNet review: 0333639
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {E_n}$ be an increasing sequence of locally convex linear topological spaces such that the dual $ {E'_n}$ of each has a Fréchet topology (not necessarily compatible with the dual system $ ({E'_n},{E_n}))$ weaker than the Mackey topology. Let $ E = \bigcup\nolimits_{n = 1}^\infty {{E_n},F} $ be a subspace of $ E$ and $ \tau $ the inductive limit convergence structure on $ E$. Conditions are given which insure that every $ \tau $-continuous linear functional on $ F$ has a $ \tau $-continuous linear extension to $ E$. This result generalizes a theorem of C. Foias and G. Marinescu.


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

  • [1] M. DeWilde, Sur un type particulier de limite inductive, Bull. Soc. Roy. Sci. Liège 35 (1966), 545-551. MR 35 #5890. MR 0215045 (35:5890)
  • [2] H. R. Fischer, Limesräume, Math. Ann. 137 (1959), 269-303. MR 22 #225. MR 0109339 (22:225)
  • [3] C. Foias and G. Marinescu, Fonctionelles linéaires dans les réunions dénombrables d'espaces de Banach réflexifs, C. R. Acad. Sci. Paris 261 (1965), 4958-4960. MR 33 #3095. MR 0194889 (33:3095)
  • [4] H. Hogbe-Nlend, Théorie des bornologies et applications, Lecture Notes in Math., Springer-Verlag, Berlin, 1971. MR 0625157 (58:30002)
  • [5] John Horvàth, Topological vector spaces and distributions. Vol. I, Addison-Wesley, Reading, Mass., 1966. MR 34 #4863. MR 0205028 (34:4863)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46A05

Retrieve articles in all journals with MSC: 46A05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0333639-7
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society