Topics in Banach Space Theory

Fernando Albiac, Nigel J. Kalton (Autoren)

Buch | Softcover

376 Seiten

2010 | Softcover reprint of hardcover 1st ed. 2006
Springer-Verlag New York Inc.
978-1-4419-2099-7 (ISBN)

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This book grew out of a one-semester course given by the second author in 2001 and a subsequent two-semester course in 2004-2005, both at the University of Missouri-Columbia. The text is intended for a graduate student who has already had a basic introduction to functional analysis; the aim is to give a reasonably brief and self-contained introduction to classical Banach space theory. Banach space theory has advanced dramatically in the last 50 years and we believe that the techniques that have been developed are very powerful and should be widely disseminated amongst analysts in general and not restricted to a small group of specialists. Therefore we hope that this book will also prove of interest to an audience who may not wish to pursue research in this area but still would like to understand what is known about the structure of the classical spaces. Classical Banach space theory developed as an attempt to answer very natural questions on the structure of Banach spaces; many of these questions date back to the work of Banach and his school in Lvov. It enjoyed, perhaps, its golden period between 1950 and 1980, culminating in the definitive books by Lindenstrauss and Tzafriri [138] and [139], in 1977 and 1979 respectively. The subject is still very much alive but the reader will see that much of the basic groundwork was done in this period.

Bases and Basic Sequences.- The Classical Sequence Spaces.- Special Types of Bases.- Banach Spaces of Continuous Functions.- L1(?)-Spaces and C(K)-Spaces.- The Lp-Spaces for 1 ? p < ?.- Factorization Theory.- Absolutely Summing Operators.- Perfectly Homogeneous Bases and Their Applications.- ?p-Subspaces of Banach Spaces.- Finite Representability of ?p-Spaces.- An Introduction to Local Theory.- Important Examples of Banach Spaces.

Erscheint lt. Verlag	19.11.2010
Reihe/Serie	Graduate Texts in Mathematics ; 233
Zusatzinfo	XI, 376 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4419-2099-4 / 1441920994
ISBN-13	978-1-4419-2099-7 / 9781441920997
Zustand	Neuware