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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.26 no.3 Antofagasta Dec. 2007

http://dx.doi.org/10.4067/S0716-09172007000300002 

 

Proyecciones Journal of Mathematics
Vol. 26, Nº 3, pp. 245-251, December 2007.
Universidad Católica del Norte
Antofagasta - Chile


THE UNIFORM BOUNDEDNESS PRINCIPLE FOR ARBITRARY LOCALLY CONVEX SPACES


CHARLES SWARTZ
New Mexico State University, U. S. A.

Correspondencia a:



Abstract
We establish uniform boundedness principle for pointwise bounded families of continuous linear operators between locally convex spaces which require no assumptions such as barrelledness on the domain space of the operators. We give applications of the result to separately continuous bilinear operators between locally convex spaces.

REFERENCES
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[LC] Li, R. and Cho, M., A Banach-Steinhaus Type Theorem Which is Valid for every Locally Convex Space, Applied Functional Anal., 1, pp. 146-147,         [ Links ](1993).
[S] Swartz, C.,An Introduction to Functional Analysis, Marcel Dekker, N.Y.,         [ Links ](1992).
[W] Wilansky, A.,Modern Methods in Topological Vector Spaces, McGraw- Hill, N. Y., (1978).
        [ Links ]

CHARLES SWARTZ
Department of Mathematics
New Mexico State University
Las Cruces, New Mexico, 88003
U. S. A.
e-mail : mailto:cswartz@nmsu.edu

Received : August 2007. Accepted : October 2007

 

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