IJPAM: Volume 16, No. 2 (2004)

ON THE PRINCIPLE OF UNIFORM BOUNDEDNESS
IN A STRICTLY ${\cal N}$-LOCALLY CONVEX SPACES

Samir Lahrech$^1$
$^1$Department of Mathematics
Faculty of Science
Mohamed I University
Oujda, 60 000, MOROCCO
e-mail: lahrech@sciences.univ-oujda.ac.ma


Abstract.In this paper we would like to establish the uniform boundedness principle for sequentially continuous linear operators in some class of locally convex spaces (strictly ${\cal N}$-locally convex spaces).

If it is possible to prove the uniform boundedness principle in such spaces, then our result will generalize the uniform boundedness principle for continuous linear operators in Banach spaces, since the class of strictly ${\cal N}$-locally convex spaces contains the class of Banach spaces.

Received: May 29, 2004

AMS Subject Classification: 47B37, 46A45

Key Words and Phrases: uniform boundedness principle, sequential continuity, strictly ${\cal N}$-locally convex spaces

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 16
Issue: 2