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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
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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.


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

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