Extending Continuous Linear Functionals in Convergence Inductive Limit Spaces

Extending Continuous Linear Functionals in Convergence Inductive Limit Spaces

Let Enbe an increasing sequence of locally convex linear topological spaces such that the dual E'nof each has a Frechet topology (not necessarily compatible with the dual system (E'n, En)) weaker than the Mackey topology. Let$E = \bigcup^\infty_{n = 1} E_n, F$be a subspace of E and τ the i...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society Vol. 43; no. 2; pp. 357 - 360
Main Authors: Kranzler, S. K., McDermott, T. S.
Format: Journal Article
Language:English
Published: American Mathematical Society 01-04-1974
Subjects:
Banach space
Frechet topologies
Mathematical theorems
Topological spaces
Topological theorems
Topology
Online Access:Get full text
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Summary:Let Enbe an increasing sequence of locally convex linear topological spaces such that the dual E'nof each has a Frechet topology (not necessarily compatible with the dual system (E'n, En)) weaker than the Mackey topology. Let$E = \bigcup^\infty_{n = 1} E_n, F$be a subspace of E and τ the inductive limit convergence structure on E. Conditions are given which insure that every τ-continuous linear functional on F has a τ-continuous linear extension to E. This result generalizes a theorem of C. Foias and G. Marinescu.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-1974-0333639-7