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Zusatztext Besides a general renovation! the text has improved the topics related to the Hahn-Banach theorem ? there is a whole new chapter on vector-valued Hahn-Banach theorems and an enlarged presentation of the Banach-Stone theorems. The text remains a nice expository book on the fundamentals of the theory of topological vector spaces. -Luis Manuel Sanchez Ruiz! Mathematical Reviews! Issue 2012aThis is a nicely written! easy-to-read expository book of the classical theory of topological vector spaces. ? The proofs are complete and very detailed. ? The comprehensive exposition and the quantity and variety of exercises make the book really useful for beginners and make the material more easily accessible than the excellent classical monographs by Köthe or Schaefer. ? this is a well-written book! with comprehensive proofs! many exercises and informative new sections of historical character! that presents in an accessible way the classical theory of locally convex topological vector spaces and that can be useful especially for beginners interested in this topic.-José Bonet! Zentralblatt MATH 1219Praise for the First Edition:This is a very carefully written introduction to topological vector spaces. But it is more. The enthusiasm of the authors for their subject! their untiring efforts to motivate and explain the ideas and proofs! and the abundance of well-chosen exercises make the book an initiation into a fascinating new world. The reader will feel that he does not get only one aspect of this field but that he really gets the whole picture.-Gottfried Köthe! Rendiconti del Circolo Matematico di Palermo! Series II! Volume 35! Number 3! September 1986 Informationen zum Autor Lawrence Narici and Edward Beckenstein are professors of mathematics at St. John’s University in New York. Klappentext With many new concrete examples and historical notes, this second edition provides one of the most thorough and up-to-date treatments of the Hahn-Banach theorem. This edition explores the theorem's connection with the axiom of choice, discusses the uniqueness of Hahn-Banach extensions, and includes an entirely new chapter on vector-valued Hahn-Banach theorems. It also considers different approaches to the Banach-Stone theorem as well as variations of the theorem. The authors trace the development of various theorems and chronicle the lives of key mathematicians, such as Stefan Banach and Eduard Helly. Zusammenfassung With many examples and historical notes, this book provides a treatment of the Hahn-Banach theorem. It explores the theorem's connection with the axiom of choice, discusses the uniqueness of Hahn-Banach extensions, and includes a chapter on vector-valued Hahn-Banach theorems. Inhaltsverzeichnis Background. Commutative Topological Groups. Completeness. Topological Vector Spaces. Locally Convex Spaces and Seminorms. Bounded Sets. Hahn–Banach Theorems. Duality. Krein–Milman and Banach–Stone Theorems. Vector-Valued Hahn–Banach Theorems. Barreled Spaces. Inductive Limits. Bornological Spaces. Closed Graph Theorems. Reflexivity. Norm Convexities and Approximation. Bibliography. Index. ...
