The Special Year in Modern Analysis at the University of Illinois was devoted to the synthesis and expansion of modern and classical analysis. The program brought together analysts from around the globe for intensive lectures and discussions, including an International Conference on Modern Analysis, held March 16–19, 1987. The Special Year's success is a tribute to the outstanding merits and professional dedication of the participants. Contributions to these Proceedings of the Special Year were solicited from the participants in order to record and disseminate the fruits of their activities. The editors are grateful to the contributors for their response, which accurately reflects the quality and substance of the Special Year. In keeping with the wide scope of topics treated, the contents of these Proceedings fell naturally into two interrelated volumes, covering “Analysis in Abstract Spaces” and “Analysis in Function Spaces”.

Thanks are due to the National Science Foundation, the Argonne Universities Association Trust Fund, the University of Illinois Campus Research Board, the University of Illinois Miller Endowment Fund, the University of Illinois Department of Mathematics, and J. Bourgain's Chair in Mathematics at the University of Illinois, without whose financial support the Special Year could not have taken place. Special thanks are also due to Professor Bela Bollobas, Consulting Editor at Cambridge University Press, and Mr. David Tranah, Senior Editor in Mathematical Sciences at Cambridge University Press, for the guidance and encouragement which made these Proceedings possible.