Non-Finite Dimensional Closed Vector Spaces of Universal Functions for Composition Operators
✍ Scribed by L.B. Gonzalez; A.M. Rodriguez
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 604 KB
- Volume
- 82
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
✦ Synopsis
Let (H(\Omega)) be the space of analytic functions on a complex region (\Omega), which is not the punctured plane. In this paper, we prove that if a sequence of automorphisms (\left{\varphi_{n}\right}{n \geqslant 0}) of (\Omega) has the property that for every compact subset (K \subset \Omega) there is a positive integer (n) such that (K \cap \varphi{n}(K)=\varnothing), then there exists an infinite dimensional closed vector subspace (F \subset H(\Omega)) such that for all (f \in F \backslash{0}) the orbit (\left{f \circ \varphi_{n}\right}_{n \geqslant 0}) is dense in (H(\Omega)). The corresponding result for the punctured plane is somewhat different and is also studied. 1995 Academic Press. Inc.