Operators and Function Theory

1. Front Matter

   Pages ii-xvi

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2. Bloch Functions: The Basic Theory

   • J. M. Anderson

   Pages 1-17

3. A Survey of Some Results on Subnormal Operators

   • John B. Conway

   Pages 19-37

4. Optimization, Engineering, and a More General Corona Theorem

   • J. William Helton

   Pages 39-40

5. Minimal Factorization, Linear Systems and Integral Operators

   • M. A. Kaashoek

   Pages 41-86

6. Ha-Plitz Operators: A Survey of Some Recent Results

   • N. K. Nikol’skii

   Pages 87-137

7. Stochastic Processes, Infinitesimal Generators and Function Theory

   • Bernt Øksendal

   Pages 139-162

8. Paracommutators and Minimal Spaces

   • Jack Peetre

   Pages 163-224

9. Decomposition Theorems for Bergman Spaces and the IR Applications

   • Richard Rochberg

   Pages 225-277

10. Operator-Theoretic Aspects of the Nevanlinna-Pick Interpolation Problem

    • Donald Sarason

    Pages 279-314

11. Cyclic Vectors in Banach Spaces of Analytic Functions

    • Allen L. Shields

    Pages 315-349

12. Interpolation by Analytic Matrix Functions

    • N. J. Young

    Pages 351-383

In the modern study of Hilbert space operators there has been an increasingly subtle involvement with analytic function theory. This is evident in the analysis of subnormal operators, Toeplitz operators and Hankel operators, for example. On the other hand the operator theoretic viewpoint of interpolation by analytic functions is a powerful one. There has been significant activity in recent years, within these enriching interactions, and the time seemed right for an overview ot the main lines of development. The Advanced Study Institute 'Operators and Function Theory' in Lancaster, 1984, was devoted to this, and this book contains ex­ panded versions (and one contraction) of the main lecture prog­ ramme. These varied articles, by prominent researchers, include, for example, a survey of recent results on subnormal operators, recent work of Soviet mathematicians on Hankel and Toeplitz operators, expositions of the decomposition theory and inter­ polation theory for Bergman, Besov and Bloch spaces, with applic­ ations for special operators, the Krein space approach to inter­ polation problems, •• and much more. It is hoped that these proceedings will bring all this lively mathematics to a wider audience. Sincere thanks are due to the Scientific Committee of the North Atlantic Treaty Organisation for the generous support that made the institute possible, and to the London Mathematical Society and the British Council for important additional support. Warm thanks also go to Barry Johnson and the L.M.S. for early guidance, and to my colleague Graham Jameson for much organisational support.

• Hilbert space
• analytic function
• banach spaces
• integral
• interpolation
• minimum
• operator

• Department of Mathematics, University of Lancaster, Lancaster, UK

  S. C. Power

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