ISOMETRIES ON BANACH SPACES VECTOR-VALUED FUNCTION SPACES by Richard J. Fleming James E. Jamison
The completion of this volume ends a project which has been on our minds for over 20 years. We began the writing of what became the first volume [137] in the fall of 1995. It has been a labor of love and we hope it will prove to be a useful addition to the literature. The original idea was to provide a full survey of the work done in characterizing the form of isometries on various Banach spaces. That turned out to be a task too vast in its extent to be done very successfully, but we have tried to touch on as many of its aspects as possible and to include a large number of references. Isometries are of fundamental importance and interest, and results about them pop up in all kinds of places.
The goal of this present volume is the same as in the earlier one, to produce a useful resource for experts in the field, as well as for others who just want to become acquainted with this part of Banach space theory. We have tried to be sensitive to the history of each topic, and so most chapters begin with a discussion of one of the earlier papers. The choice of material to exposit is always difficult, and in most cases we have tried to move through successive developments, so that often the theorems of later sections actually include the earlier ones. We have tried to expose a variety of methods and tools used in the characterizations, even though the end result is often predictable. The notes and remarks are intended to fill in for some of the omissions.
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