Semicontinuity of nullity or deficiency implies normability of the space
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- by John M. Hosack
- Proc. Amer. Math. Soc. 30 (1971), 321-323
- DOI: https://doi.org/10.1090/S0002-9939-1971-0290078-2
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Abstract:
In this paper the upper semicontinuity of nullity and deficiency on locally convex spaces is examined. If either is semicontinuous in the topology of uniform convergence on bounded sets on $L(X)$, then X is normable. If the invertible elements in $L(X)$ are open, then X is normable. The results are applied to topological algebras.References
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Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 321-323
- MSC: Primary 46.10; Secondary 47.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0290078-2
- MathSciNet review: 0290078