The compact approximation property for spaces of holomorphic mappings on Frechet spaces


Caliskan E., Rueda P.

REVISTA MATEMATICA COMPLUTENSE, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2020
  • Doi Number: 10.1007/s13163-019-00344-9
  • Title of Journal : REVISTA MATEMATICA COMPLUTENSE

Abstract

In this paper, the compact approximation property on Frechet spaces is characterized in terms of holomorphic mappings. We show that a Frechet space E has the compact approximation property if and only if every holomorphic mapping on a balanced open subset U subset of E with values in a Frechet space can be approximated uniformly on compact subsets of U by compact holomorphic mappings. This extends the well-known linear characterization to the holomorphic setting. We also give characterizations of the compact approximation property in terms of bounded holomorphic mappings on Banach spaces.