Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advantages of systems consisting of characters on compact Abelian groups. Probabilistic concepts such as random variables and martingales are employed and Ramsey's theorem is used to study the theory of super-reflexivity. The text yields a detailed insight into concepts including type and co-type of...

make it look much more logical, but actually it happens quite differently. Atiyah 2004 ] The monographs A. F. Monna: Functional Analysis in Historical Perspective (1973), and J. Dieudonne: History of Functional Analysis (1981), as well as all articles devoted to the history of functional analysis deal only with the development before 1950. Now the time has come to cover the second half of the twentieth century too. I have undertaken this adventure. Let me introduce myself by telling you that I received my M. Sc. degree in 1958, just at the time when the renaissance of Banach space theory...

This book describes the interplay between orthonormal expansions and Banach space geometry.

Ich hatte es oft schmerzlich empfunden, daB bei der Schnelligkeit der Entwicklung unserer Wissenschaft die Zeit vOliiber ist, wo wir die gr6Bte Weisheit in den iiltesten Biichern fanden und so das Gliick genieBen konnten, das BewuBtsein der Belehrung mit dem Gefiihl der Pietat fiir das Ehrwiirdige zu verbinden. ERHARD SCHMIDT, 1919 Dieser Band des "TEUBNER-ARCHIVs zur Mathematik" enthalt die entscheiden den Arbeiten uber "Lineare Integralgleichungen und Gleichungen mit unendlich vielen Unbekannten," die DAVID HILBERT und sein Schuler ERHARD SCHMIDT in der Zeit von 1904 bis 1910 publiziert...

VI closely related to finite dimensional locally convex spaces than are normed spaces. In order to present a clear narrative I have omitted exact references to the literature for individual propositions. However, each chapter begins with a short introduction which also contains historical remarks. Deutsche Akademie der vVissenschaften zu Berlin Institut fur Reine Mathematik Albrecht Pietsch Foreword to the Second Edition Since the appearance of the first edition, some important advances have taken place in the theory of nuclear locally convex spaces. Firsts there is the Universality Theorem...