logo_acta

Acta Mathematica Vietnamica

PROPERTY Ω AND HOLOMORPHIC FUNCTIONS WITH VALUES IN A PSEUDOCONVEX SPACE HAVING A STEIN MORPHISM INTO A COMPLEX LIE GROUP

NGUYEN MINH HA, THAI THUAN QUANG

Abstract

It is shown that a Fréchet-Schwartz space E with an absolute basis has the property Ω if and only if every holomorphic function on D×E with values in a pseudoconvex space having a Stein morphism into a complex Lie group, where D is a Stein space, is of uniform type. In the scalar case, where E is a nuclear Fréchet space, the result was established by Meise and Vogt [5].