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.

Additive combinatorics by Terence Tao, Van H. Vu

Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate level text will allow students and researchers easy entry into this fascinating field.