By Spiros A. Argyros, Stevo Todorcevic

This publication introduces graduate scholars and resarchers to the research of the geometry of Banach areas utilizing combinatorial tools. The combinatorial, and specifically the Ramsey-theoretic, method of Banach area concept isn't really new, it may be traced again as early because the Nineteen Seventies. Its complete appreciation, notwithstanding, got here basically over the past decade or so, after essentially the most very important difficulties in Banach house thought have been solved, equivalent to, for instance, the distortion challenge, the unconditional simple series challenge, and the homogeneous area challenge. The ebook covers almost all these advances, yet certainly one of its basic reasons is to debate the various contemporary advances that aren't found in survey articles of those components. We express, for instance, find out how to introduce a conditional constitution to a given Banach area lower than development that permits us to actually prescribe the corresponding area of non-strictly singular operators. We additionally practice the Nash-Williams thought of fronts and obstacles within the learn of Cezaro summability and unconditionality found in uncomplicated sequences within a given Banach house. We additional supply a close exposition of the block-Ramsey concept and its fresh deep alterations proper to the Banach area conception because of Gowers.