The Theory of H(b) Spaces: Volume 1

Emmanuel Fricain is a Professor in the Laboratoire Paul Painlevé at Université Lille 1. A part of his research focuses on the interaction between complex analysis and operator theory, which is the main matter of this book. He has a long experience of teaching numerous graduate courses on different aspects of analytic Hilbert spaces and has published several papers on H(b) spaces in high-quality journals, making him a world specialist in this subject. Javad Mashreghi is a Professor of Mathematics at Laval University, Québec, where he has been selected Star Professor of the Year five times for excellence in teaching. His main fields of interest are complex analysis, operator theory and harmonic analysis.

• List of figures; Preface; List of symbols; Important conventions; 1. *Normed linear spaces and their operators; 2. Some families of operators; 3. Harmonic functions on the open unit disc; 4. Analytic functions on the open unit disc; 5. The corona problem; 6. Extreme and exposed points; 7. More advanced results in operator theory; 8. The shift operator; 9. Analytic reproducing kernel Hilbert spaces; 10. Bases in Banach spaces; 11. Hankel operators; 12. Toeplitz operators; 13. Cauchy transform and Clark measures; 14. Model subspaces KΘ; 15. Bases of reproducing kernels and interpolation; Bibliography; Index.

'This two volume monograph is a compendium of the H(b) spaces that will be of interest to both graduate students and practicing mathematicians interested in function-theoretic operator theory. There are 31 chapters between the two volumes and a detailed bibliography consisting of 766 entries. The first volume is devoted to general function-theoretic operator theory (and indeed is a useful reference in its own right) while the second volume is more specialized and contains an in-depth survey of H(b)H(b) theory and related ideas.' Steve Deckelman, MAA Reviews