Topological Vector Spaces

ISBN-13: 9781584888666 / Angielski / Twarda / 2010 / 628 str.

Lawrence Narici;Edward Beckenstein

Opis

With many new concrete examples and historical notes, Topological Vector Spaces, 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 book covers locally convex spaces; barreled, bornological, and webbed spaces; and reflexivity. It traces the development of various theorems from their earliest beginnings to present day, providing historical notes to place the results in context. The authors also chronicle the lives of key mathematicians, including Stefan Banach and Eduard Helly. Suitable for both beginners and experienced researchers, this book contains an abundance of examples, exercises of varying levels of difficulty with many hints, and an extensive bibliography and index.

Spis treści

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.

O autorze

Lawrence Narici and Edward Beckenstein are professors of mathematics at St. John’s University in New York.