Topics in Banach Space Theory
Springer International Publishing (Verlag)
978-3-319-31555-3 (ISBN)
This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces.
From the reviews of the First Edition:
"The authors of the book...succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly... It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments... I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book..."-Gilles Godefroy, Mathematical Reviews
Fernando Albiac is Professor of mathematical analysis at the Public University of Navarra in Pamplona Spain. His current research focuses primarily on geometric nonlinear functional analysis and greedy approximation with respect to bases in Banach spaces. Nigel Kalton was Professor of Mathematics at the University of Missouri, Columbia. He wrote over 250 articles with nearly 100 different co-authors, and was the recipient of the 2004 Banach Medal of the Polish Academy of Sciences.
lt;p>1. Bases and Basic Sequences.- 2. The Classical Sequence Spaces.- 3. Special Types of Bases.- 4. Banach Spaces of Continuous Functions.- 5. L_{1}(mu )-Spaces and mathcal C(K)-Spaces.- 6. The Spaces L_{p} for 1le p^I Basic probability in use.- Appendix J Generalities on Ultraproducts.- Appendix K The Bochner Integral abridged.- List of Symbols.- References.- Index
"This excellent book is highly recommended to all graduate students and up who want to experience the beauty of the Banach space theory." (Marián Fabian, Mathematical Reviews, June, 2017)
Erscheinungsdatum | 08.10.2016 |
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Reihe/Serie | Graduate Texts in Mathematics |
Zusatzinfo | XX, 508 p. 23 illus., 14 illus. in color. |
Verlagsort | Cham |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Schlagworte | Banach Space Theory • Continuous functions • Factorization Theory • Functional Analysis • greedy approximation • Lp-spaces • mathematics and statistics • nonlinear geometry of Banach spaces |
ISBN-10 | 3-319-31555-2 / 3319315552 |
ISBN-13 | 978-3-319-31555-3 / 9783319315553 |
Zustand | Neuware |
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