Details

Autor(en) / Beteiligte

• Çalışkan, E.
• Rueda, P.

Titel

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

Ist Teil von

• Revista matemática complutense, 2021, Vol.34 (1), p.185-201

Ort / Verlag

Cham: Springer International Publishing

Erscheinungsjahr

2021

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper, the compact approximation property on Fréchet spaces is characterized in terms of holomorphic mappings. We show that a Fréchet space E has the compact approximation property if and only if every holomorphic mapping on a balanced open subset U ⊂ E with values in a Fréchet 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.