The MathNet Korea
Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Glasnik Matematicki Serja III.
( Vol. 34 NO.2 / (1999))
A Necessary and Sufficient Condition for a Space to be Infrabarrelled or Polynomially Infrabarrelled
Miguel Caldas Cueva, Dinamerico P. Pombo Jr,
Pages. 263-265
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 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.
Contents
Key words Locally convex spaces, continuous $m$-homogeneous polynomials, topology of bounded convergence, equicontinuous sets
Mathmatical Subject Classification 46E40