History of Banach Spaces and Linear Operators (eBook)

Albrecht Pietsch (Autor)

eBook Download: PDF

2007 | 2007
XXIII, 855 Seiten
Birkhäuser Boston (Verlag)
978-0-8176-4596-0 (ISBN)

Infos

Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.

---

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 started. Thus I have ?rst-hand experience of the progress achieved during the past 50 years. Due to the explosion of knowledge, writing about functional analysis as a whole seems to be no longer possible. Hence this book is focused on Banach spaces and (abstract bounded) linear operators. Other subjects such as topologies, measures and integrals, locally convex linear spaces, Banach lattices, and Banach algebras are treated only in so far as they turn out to be relevant for this purpose. The interplay with set theory is described carefully: Which axioms are needed in order to prove the Hahn-Banach theorem? Results about non-self-adjoint operators on Hilbert spaces have been a source of inspiration for the theory of operators on Banach spaces. Such topics are discussed in great detail. However, I have omitted almost all operator-theoretic considerations that depend decisively on the existence of an inner product.

Inhalt

Contents 6
Preface 13
Notation and Terminology 17
Introduction 18
1 The Birth of Banach Spaces 23
2 Historical Roots and Basic Results 47
3 Topological Concepts – Weak Topologies 78
4 Classical Banach Spaces 108
5 Basic Results from the Post-Banach Period 180
6 Modern Banach Space Theory – Selected Topics 310
7 Miscellaneous Topics 572
8 Mathematics Is Made by Mathematicians 611
Chronology 695
Original Quotations 702
Bibliography 705
Index 856

Produkt-Details

• Erscheint lt. Verlag: 31.12.2007
• Zusatzinfo: XXIII, 855 p. 82 illus.
• Verlagsort: Boston
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Themenwelt: Technik
• Schlagworte: Banach space • bounded linear operators • Functional Analysis • Harmonic Analysis • History of Mathematics
• ISBN-10: 0-8176-4596-9 / 0817645969
• ISBN-13: 978-0-8176-4596-0 / 9780817645960