Completely continuous multilinear operators on $C(K)$ spaces

Abstract

Given a $k$-linear operator $T$ from a product of $C(K)$ spaces into a Banach space $X$, our main result proves the equivalence between $T$ being completely continuous, $T$ having an $X$-valued separately $\omega ^*-\omega ^*$ continuous extension to the product of the biduals and $T$ having a regular associated polymeasure. It is well known that, in the linear case, these are also equivalent to $T$ being weakly compact, and that, for $k>1$, $T$ being weakly compact implies the conditions above but the converse fails.

Locations

• Proceedings of the American Mathematical Society - View - PDF
• LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) - View - PDF