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

Caliskan E., Rueda P.

REVISTA MATEMATICA COMPLUTENSE, cilt.34, sa.1, ss.185-201, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s13163-019-00344-9
  • Dergi Adı: REVISTA MATEMATICA COMPLUTENSE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.185-201
  • Anahtar Kelimeler: Compact approximation property, Holomorphic mappings, Homogeneous polynomials
  • İstanbul Üniversitesi Adresli: Hayır

Özet

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.