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, acac 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.S.C. Power. In non-tangential convergence one considers angles in A with vertex at a boundary point w. (Stolz angles). ... They show the precise connection between the kind of subregions in which approach to the boundary is permitted, and the size of the exceptional set where the limit fails to exist. As regards cyclic vectors, we consider first the two test questions: 1) If ... 281] L. Brown and the author show that l) has an affirmative answer if, in addition, one assumes that g e M (D).
|Title||:||Operators and Function Theory|
|Publisher||:||Springer Science & Business Media - 2012-12-06|