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Semicontinuity of nullity or deficiency implies normability of the space


Author: John M. Hosack
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0290078-2
Keywords: Normability of locally convex spaces or algebras, semicontinuity of deficiency or nullity, invertible elements
Article copyright: © Copyright 1971 American Mathematical Society

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