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

Caliskan E., Rueda P.

REVISTA MATEMATICA COMPLUTENSE, vol.34, no.1, pp.185-201, 2021 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1007/s13163-019-00344-9
  • Journal Name: REVISTA MATEMATICA COMPLUTENSE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.185-201
  • Keywords: Compact approximation property, Holomorphic mappings, Homogeneous polynomials
  • Istanbul University Affiliated: No

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.