Stein manifolds M for which O(M) has the property Ω-tilda

Abstract

In this note, we consider the linear topological invariant Ω-tilda for Fréchet spaces of global analytic functions on Stein manifolds. We show that O(M), for a Stein manifold M, enjoys the property Ω-tilda if and only if every compact subset of M lies in a relatively compact sublevel set of a bounded plurisubharmonic function defined on M. We also look at some immediate implications of this characterization.

Dedicated to Mikhail Mikhaylovich Dragilev on the occasion of his 90 th birthday. To appear in Vladikavkaz Mathematical Journal (VMJ)