Banach Spaces of Analytic Functions
About this Title
Rita A. Hibschweiler and Thomas H. MacGregor, Editors
This volume is focused on Banach spaces of functions analytic in the open unit disc, such as the classical Hardy and Bergman spaces, and weighted versions of these spaces. Other spaces under consideration here include the Bloch space, the families of Cauchy transforms and fractional Cauchy transforms, BMO, VMO, and the Fock space. Some of the work deals with questions about functions in several complex variables.
Multiplication operators, composition operators and weighted composition operators form a central topic of the volume. This topic has been an extensive area of research for the past twenty years. This volume includes results characterizing bounded, compact and isometric composition operators in various settings.
Graduate students who are interested in analysis will find an overview of current work in the field. Specialists will find interesting questions and new methods, as well as familiar ideas (such as composition operators) seen in new settings or in more general form. Mathematicians with an interest in modern analysis will gain insight into the interplay between function theory and operator theory which is central to this work.
Graduate students and research mathematicians interested in function theory and operator theory.
Table of Contents
- Joseph A. Cima – A note on the life of Alec Matheson and some of his work [MR 2408229]
- Joseph A. Cima – On the inverse of an analytic mapping [MR 2408230]
- Joel Cohen and Flavia Colonna – Isometric composition operators on the Bloch space in the polydisk [MR 2408231]
- Oleg Eroshkin – Pluripolarity of manifolds [MR 2408232]
- Richard Fournier and Luis Salinas – On a question of Brézis and Korevaar concerning a class of square-summable sequences [MR 2408233]
- Zdeňka Guadarrama and Dmitry Khavinson – Approximating $\overline z$ in Hardy and Bergman norms [MR 2408234]
- Don Hadwin and Eric Nordgren – A general view of multipliers and composition operators. II [MR 2408235]
- Don Hadwin and Hassan Yousefi – A general view of BMO and VMO [MR 2408236]
- R. A. Hibschweiler – Order bounded weighted composition operators [MR 2408237]
- T. H. MacGregor – Fractional Cauchy transforms and composition [MR 2408238]
- Alec L. Matheson – Continuous functions in star-invariant subspaces (abstract) [MR 2408239]
- William T. Ross – Indestructible Blaschke products [MR 2408240]
- James Tung – On Taylor coefficients and multipliers in Fock spaces [MR 2408241]