On complex Banach manifolds similar to Stein manifolds

TL;DR

This paper defines a class of complex Banach manifolds analogous to Stein manifolds, characterizing them as biholomorphic to closed split submanifolds of separable Banach spaces, thus extending Stein manifold concepts to infinite dimensions.

Contribution

It introduces an abstract axiomatic framework for complex Banach manifolds similar to Stein manifolds, providing a new characterization in infinite-dimensional complex analysis.

Findings

Characterization of complex Banach manifolds as biholomorphic to closed split submanifolds

Extension of Stein manifold properties to infinite-dimensional spaces

Axiomatic definition aligning with classical Stein manifold concepts

Abstract

We give an abstract definition, similar to the axioms of a Stein manifold, of a class of complex Banach manifolds in such a way that a manifold belongs to the class if and only if it is biholomorphic to a closed split complex Banach submanifold of a separable Banach space.