Extending continuous linear functionals in convergence inductive limit spaces
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- by S. K. Kranzler and T. S. McDermott PDF
- Proc. Amer. Math. Soc. 43 (1974), 357-360 Request permission
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
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Additional Information
- © Copyright 1974 American Mathematical Society
- 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