Property Ω and holomorphic functions with values in a pseudoconvex space having Stein morphism into a complex Lie group

Abstract

It is shown that a nuclear Frechet space E with a Schauder basis has the property ΩF if and only if there exists a compact balanced convex set B in E such that every holomorphic function on (EB, τE), where EB is the Banach space spanned by B and τE is the topology of EB induced by the topology of E, with values in any pseudoconvex space having a Stein morphism into a complex Lie group, can be extended holomorphically to E. For the scalar case the proof was provided by Meise and Vogt [4].

Keywords

• holomorphic function of uniform type
• pseudoconvex space
• stein morphism
• complex lie group