Behavior of holomorphic mappings on p-compact sets in a Banach space

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. 2010 Mathematics Subject Classification. Primary 46G20; Secondary 46B28, 46G25. Key words and phrases. Banach spaces, p-compact sets, homogeneous polynomials, holomorphic mappings.