Local description of closed ideals and submodules of analytic functions of one variable.~II

I. F. Krasichkov-Ternovskii

Izvestiya. Mathematics , Tome 14 (1980) no. 2, pp. 289-316

Résumé

Let $P$ be a topological module (over the ring of polynomials) of vector-valued functions $f\colon G\to\mathbf C^q$ holomorphic in a domain $G\subset\mathbf C$. In the first part of this article it was established that to solve the local description problem for closed submodules of $P$ it suffices to verify two properties – stability and saturation. In the present second part various methods of carrying out this verification are elaborated. Conditions are presented under which closed submodules are stable and saturated and, consequently, local. In particular a wide class of locally convex algebras of analytic functions which admit local description of their closed ideals is isolated. Bibliography: 15 titles.