Miguel Caldas Cueva

032. A necessary and sufficient condition for a space to be infrabarrelled…

Full Title: A necessary and sufficient condition for a space to be infrabarrelled or polynomially infrabarrelled
Math. Journal: Glasnick Matematicki , Croatia, 34 (1999), 263-265.
Authors: Caldas, M. and Pombo, D.

Abstract
A locally convex space E is polynomially barrelled (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 continuous linear mappings from E into F (resp. the space of all continuous m-homogeneous polynomials from E into F) is quasi-complete for the topology of bounded convergence.