Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 0290078
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46.10, 47.00

Retrieve articles in all journals with MSC: 46.10, 47.00


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0290078-2
PII: S 0002-9939(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