Glasnik Matematicki, Vol. 34, No.2 (1999), 263-265.

A NECESSARY AND SUFFICIENT CONDITION FOR A SPACE TO BE INFRABARRELLED OR POLYNOMIALLY INFRABARRELLED

Miguel Caldas Cueva and Dinamerico P. Pombo Jr.

Abstract.   A locally convex space E is infrabarrelled (resp. polynomially infrabarrelled) if and only if, for every Banach space F (resp. for every positive integer m and for every Banach space F), the space of all continous linear mappings from E into F (resp. the space of all continuous m-homogeous polynomials form E into F) is quasi-complete for the topology of bounded convergence.

1991 Mathematics Subject Classification.   46E40.

Key words and phrases.   Locally convex spaces, continuous m-homogeneous polynomials, topology of bounded convergence, equicontinuous sets.