BEHAVIOR OF HOLOMORPHIC MAPPINGS ON p-COMPACT SETS IN A BANACH SPACE

Abstract

We study the behavior of holomorphic mappings on p-compact sets in Banach spaces. We show that the image of a p-compact set by an entire mapping is a p-compact set. Some results related to the localization of p-compact sets in the predual of homogeneous polynomials are also obtained. Finally, the size of p-compactness of the image of the unit ball by p-compact linear operators is studied.