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OverviewOne 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. The main goals of this book are to: -introduce 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, -aim the text at graduate students and researchers who have a foundation in Banach space theory, - expose the reader to some current avenues of research in biorthogonal systems in Banach spaces, -provide notes and exercises related to the topic, suggest open problems and possible new directions of research. Numerous exercises are included, and the only prerequisites are a basic background in functional analysis. Full Product DetailsAuthor: Petr Hajek , Vicente Montesinos Santalucia , Jon Vanderwerff , Vaclav ZizlerPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 2008 Dimensions: Width: 15.50cm , Height: 1.80cm , Length: 23.50cm Weight: 0.551kg ISBN: 9781441923950ISBN 10: 1441923950 Pages: 339 Publication Date: 08 September 2011 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsReviewsFrom 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) 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) "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)" Author InformationTab Content 6Author Website:Countries AvailableAll regions |