Operator-weighted composition operators between weighted spaces of vector-valued analytic functions

• Published in: Annales Academiae Scientiarum Fennicae Mathematica
• Main Authors: Bonet Solves, José Antonio, Gómez Collado, María del Carmen, Jornet Casanova, David, Wolf, Elke
• Other Authors: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada, Generalitat Valenciana, Universitat Politècnica de València, Ministerio de Ciencia e Innovación
• Format: Article in Journal/Newspaper
• Language: English
• Published: Suomalainen Tiedeakatemia (Finnish Academy of Science and Letters) 2012
• Subjects: Composition operators; Weighted spaces of analytic fucntions; Spaces of vector-valued analytic functions; Locally convex spaces; Kothe echelon spaces; MATEMATICA APLICADA; Psi; tylli
• Online Access: http://hdl.handle.net/10251/40476; https://doi.org/10.5186/aasfm.2012.3723

We investigate several properties of operator-weighted composition maps W-psi,W-phi f (right bar arrow) psi(f o phi) on unweighted H (D, X) and weighted H-nu(infinity) (D, X) spaces of vector-valued analytic functions on the unit disc D. Here phi is an analytic self-map of D and psi is an analytic operator-valued function on D. We characterize when the operator is continuous, maps a neighbourhood into a bounded set or maps bounded sets into relatively compact sets. In this way we extend results due to Laitila and Tylli for the case of Banach valued functions. This more general setting permits us to compare the results in the unweighted and weighted cases. New examples are provided, especially when the spaces X and Y are Kothe echelon spaces. They show the differences between the present setting and the case of functions taking values in Banach spaces. The research of the first three authors was partially supported by MEC and FEDER Project MTM2010-15200, by GVA, Projects GV/2010/040 and Prometeo/2008/101, and Universidad Politecnica de Valencia, Project Ref. 2773. Bonet Solves, JA.; Gómez Collado, MDC.; Jornet Casanova, D.; Wolf, E. (2012). Operator-weighted composition operators between weighted spaces of vector-valued analytic functions. Annales Academiae Scientiarum Fennicae. Mathematica. 37:319-338. https://doi.org/10.5186/aasfm.2012.3723 S 319 338 37