ON A STEIN MANIFOLD THE DOLBEAULT COMPLEX SPLITS IN POSITIVE DIMENSIONS

Abstract

In this paper we find necessary and sufficient conditions for the operator, acting in the Dolbeault complex of an analytic locally free sheaf of finite type on a complex manifold, to split in a given dimension, i.e. to possess a linear continuous right inverse operator. In particular, from this it follows that on a Stein manifold the operator always splits in all positive dimensions, while it does not split in dimension zero. We also consider some questions connected with this; in particular, the splitting of operators in the Frechet spaces and the splitting of the de Rham complex on a differentiable manifold.Bibliography: 11 items.