IJPAM: Volume 13, No. 3 (2004)

CONTINUITY OF OPERATORS ON
TOPOLOGICAL VECTOR SPACES

Diomedes Barcenas
Department of Mathematics
Faculty of Sciences
University of Los Andes
Mérida 5101, VENEZUELA
e-mail: barcenas@ciens.ula.ve


Abstract.In this paper we characterize linear and continuous operators from real Frechet spaces $\X$ into real topological vector spaces $\Y$ as those additive operators which apply bounded sets in $\X$ onto bounded sets in $\Y$. As a consequence, additive measurable functions between real finite dimensional spaces are continuous. Furthermore we remove the homogeneity hypothesis from the classical Closed Graph Theorem.

Received: February, 27, 2004

AMS Subject Classification: 46A30, 57N17, 46M35, 47H07

Key Words and Phrases: topological vector spaces, linear and continuous operator, Frechet spacse, real finite dimensional spaces, Closed Graph Theorem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 13
Issue: 3