Biorthogonal Systems in Banach Spaces - Hajek, Petr;Montesinos Santalucia, Vicente;Vanderwerff, Jon
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  • Broschiertes Buch

This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces. It achieves this in a manner accessible to graduate students and researchers who have a foundation in Banach space theory. The authors have included numerous exercises, as well as open problems that point to possible directions of research. …mehr

Produktbeschreibung
This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces. It achieves this in a manner accessible to graduate students and researchers who have a foundation in Banach space theory. The authors have included numerous exercises, as well as open problems that point to possible directions of research.
  • Produktdetails
  • CMS Books in Mathematics
  • Verlag: Springer / Springer New York / Springer, Berlin
  • 2008
  • Seitenzahl: 360
  • Erscheinungstermin: 8. September 2011
  • Englisch
  • Abmessung: 235mm x 155mm x 19mm
  • Gewicht: 546g
  • ISBN-13: 9781441923950
  • ISBN-10: 1441923950
  • Artikelnr.: 32213757
Autorenporträt
One of the fundamental questions of Banach space theory is whether every Banach space has a basis. A space with a basis gives us a sense of familiarity and concreteness, and perhaps a chance to attempt the classification of all Banach spaces and other problems. This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces, in a manner accessible to graduate students and researchers with a foundation in Banach space theory. Numerous exercises are included, and the only prerequisites are a basic background in functional analysis.
Inhaltsangabe
Separable Banach Spaces.- Universality and the Szlenk Index.- Review of Weak Topology and Renormings.- Biorthogonal Systems in Nonseparable Spaces.- Markushevich Bases.- Weak Compact Generating.- Transfinite Sequence Spaces.- More Applications.
Rezensionen
From the reviews:

"This monograph is devoted to the study of the different types of coordinate systems that may exist in infinite-dimensional Banach spaces. ... will certainly become a great reference book for specialists in nonseparable Banach space theory. Its contents are comprehensive and perfectly up to date. Very recent results are included and several proofs are simplified and given with their optimal form. It must be mentioned that this book is also accessible to graduate students and young researchers willing to discover this area." (Gilles Lancien, Mathematical Reviews, Issue 2008 k)

"The book under review contains a clear, detailed and self-contained exposition of the modern state-of-the-art in the biorthogonal systems theory. ... one of their goals is to attract young mathematicians to Banach space theory. In my opinion, the book perfectly serves this purpose. ... Every chapter contains an exercises section. Exercises ... are supplied with hints and references to the corresponding literature."(Vladimir Kadets, Zentralblatt MATH, Vol. 1136 (14), 2008)