English

Stein manifolds M for which O(M) has the property {\Omega}-tilda

Complex Variables 2014-03-20 v1

Abstract

In this note, we consider the linear topological invariant {\Omega}-tilda for Fr\'echet spaces of global analytic functions on Stein manifolds. We show that O(M), for a Stein manifold M, enjoys the property {\Omega}-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.

Keywords

Cite

@article{arxiv.1312.2760,
  title  = {Stein manifolds M for which O(M) has the property {\Omega}-tilda},
  author = {Aydın Aytuna},
  journal= {arXiv preprint arXiv:1312.2760},
  year   = {2014}
}

Comments

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