Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2025-01-03T17:39:38.729Z Has data issue: false hasContentIssue false
  • English
  • Français

The closed graph theorem without category

Published online by Cambridge University Press:  17 April 2009

Charles Swartz
Charles Swartz
Affiliation:
Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003, United States of America.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that a diagonal theorem of P. Antosik can be used to give a proof of the Closed Graph Theorem for normed spaces which does not depend upon the Baire Category Theorem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 2 , October 1987 , pp. 283 - 287
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Antosik, P. and Swartz, C., Matrix methods in analysis, Lecture Notes in Mathematics 1113, Springer-verlag, Heidelberg, 1985.CrossRefGoogle Scholar
[2]Dunford, N. and Schwartz, J., Linear operators I, Interscience, N.Y., 1958.Google Scholar
[3]Gohberg, I. and Goldberg, S., Basic operator theory, Birkhäuser, Boston, 1981.CrossRefGoogle Scholar
[4]Klis, C., “An example of noncomplete nonned (K)-space”, Bull. Acad. Polon. Sci. 26 (1978), 415–420.Google Scholar
[5]Lorentz, G.G., Approximation of functions, (Holt, Rinehart and Winston, New York, 1966).Google Scholar
[6]Pap, E., “Functional analysis with the H-convergence”, (preprint)Google Scholar
[7]Robertson, A. and Robertson, W., Topological vector spaces, Cambridge University Press, Cambridge, 1964.Google Scholar
[8]Taylor, A. and Lay, D., Introduction to functional analysis, (John Wiley, N.Y., 1980).Google Scholar