Linear topological structure of closed ideals in weighted algebras of entire functions
Let E be a weighted (DFN)- (resp. FN)) algebra of entire functions in one variable. It is shown that all non-trivial closed ideals in E are linearly homeomorphic to E, provided \(E_ b'\) (resp. E) is isomorphic to a power series space. This hypothesis is satisfied for most of the relevant examples. The proof of the case of infinite type combines a theorem of \textit{Krone} [On projections in power series spaces and the existence of bases, preprint] with a result of the author stating that each closed ideal in E admits two algebraic generators [Mich. Math. J. 34, 441-450 (1987)]. To apply Krone's result, it is shown that E is stable provided \(E_ b'\) (resp. E) is isomorphic to a power series space of indefinite type. In the case of finite type, a result of Mityagin and Henkin in the formulation of \textit{D. Vogt} [Manuscr. Math. 37, 269-301 (1982; Zbl 0512.46003)] is used instead of Krone's theorem.
weighted (DFN)-algebra of entire functions
scientific article; zbMATH DE number 4017645
scientific article