Perfect Measures, Nuclear Spaces and the Convex Compactness Property

• Jorge Vielma B. Departamento de Matemáticas. Facultad de Ciencias. Universidad de Los Andes. Mérida

Keywords: P-spaces, K-spaces, Do-spaces, real-compact spaces, convex compactness property, nuclear spaces

Abstract

It is proved that for certain kinds of K-spaces $X$, the spaces $(C_{b}(X,E),\beta_{p})$ has the convex compactness property if $E$ is a Banach space. Also, if $X$ is a real-compact K-spaces then $(C_{b}(X,E),\beta_{p})$ is a nuclear space if and only if $X$ is finite and $E$ is finite dimensional.

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