Glasnik Matematicki, Vol. 33, No.1 (1998), 93-96.

ON A CHARACTERIZATION OF POLYNOMIALLY BARRELED SPACES

Miguel Caldas Cueva and Dinamerico P. Pombo Jr.

Abstract.   A locally convex space E is polynomially barrelled if and only if, for every positive integer m and for every Banach space F, the space of all continuous m-homogeneous polynomials from E into F is quasi-complete for the topology of pointwise convergence.

1991 Mathematics Subject Classification.   46E40.

Key words and phrases.   Locally convex spaces, continuous m-homogeneous polynomials, topology of pointwise convergence, equicontinuous sets, closed graph theorem.