Overview

The present book is a self-contained text which leads the reader through all the important aspects of the theory of locally convex vector spaces over nonarchimedean fields. One can observe an increasing interest in methods from nonarchimedean functional analysis, particularly in number theory and in the representation theory of p-adic reductive groups. The book gives a concise and clear account of this theory, it carefully lays the foundations and also develops the more advanced topics. Although the book will be a valuable reference work for experts in the field, it is mainly intended as a streamlined but detailed introduction for researchers and graduate students who wish to apply these methods in different areas.

Full Product Details

Author:   Peter Schneider
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2002 ed.
Dimensions:   Width: 15.60cm , Height: 1.10cm , Length: 23.40cm
Weight:   0.930kg
ISBN:  

9783540425335

ISBN 10:   3540425330
Pages:   156
Publication Date:   20 November 2001
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

Table of Contents

I. Foundations.- Nonarchimedean Fields; Seminorms; Normed Vector Spaces; Locally Convex Vector Spaces; Constructions and Examples; Spaces of Continuous Linear Maps; Completeness; Fréchet Spaces; the Dual Space. - II. The Structure of Banach Spaces.- Structure theorems; Non-Reflexivity.- III. Duality Theory.- C-Compact and Compactoid Submodules; Polarity; Admissible Topologies; Reflexivity; Compact Limits.- IV. Nuclear Maps and Spaces.- Topological Tensor Products; Completely Continuous Maps; Nuclear Spaces; Nuclear Maps; Traces; Fredholm Theory.- References.- Index, Notations.

Reviews

From the reviews of the first edition: <p> It is the first textbook seriously covering locally convex theory over K, so a ] it is most welcome. a ] the book is self-contained, complete with all proofs, and therefore attractive also to those who are not acquainted with the above area. a ] The book is well-written, with care for details. Recommended. (W.H. Schikhof, Jahresbericht der Deutschen Mathematiker Vereinigung, Vol. 106 (1), 2004) <p> The book under review is a self-contained text concerning the theory of locally convex spaces over non-Archimedean fields. a ] The book is carefully written and incorporates for the first time results that have only appeared in papers. It will be a valuable reference work either for specialists or for non-specialists in the field. (DinamA(c)rico P. Pombo, Jr., Mathematical Reviews, Issue 2003 a) <p> Functional analysis over nonarchimedean fields has become an area of growing interest a ] . In the present book the author gives a concise and clear account of this theory, carefully lays the foundations, and also develops the more advanced topics. a ] This book gives a streamlined introduction for researchers and graduate students who want to apply these methods to other areas, and it would probably also provide a valuable reference source for researchers in the field. (Anton Deitmar, Bulletin of the London Mathematical Society, Vol. 34, 2002) <p> The present book is a self-contained text which leads the reader through all the important aspects of the theory of locally convex vector spaces over nonarchimedean fields. a ] The book gives a concise and clear account of this theory, it carefully lays the foundations and also develops the moreadvanced topics. Although the book will be a valuable reference work for experts in the field, it is mainly intended as streamlined but detailed introduction for researchers and graduate students a ] . (La (TM)Enseignement Mathematique, Vol. 48 (1-2), 2002)

From the reviews of the first edition: It is the first textbook seriously covering locally convex theory over K, so ... it is most welcome. ... the book is self-contained, complete with all proofs, and therefore attractive also to those who are not acquainted with the above area. ... The book is well-written, with care for details. Recommended. (W.H. Schikhof, Jahresbericht der Deutschen Mathematiker Vereinigung, Vol. 106 (1), 2004) The book under review is a self-contained text concerning the theory of locally convex spaces over non-Archimedean fields. ... The book is carefully written and incorporates for the first time results that have only appeared in papers. It will be a valuable reference work either for specialists or for non-specialists in the field. (Dinamerico P. Pombo, Jr., Mathematical Reviews, Issue 2003 a) Functional analysis over nonarchimedean fields has become an area of growing interest ... . In the present book the author gives a concise and clear account of this theory, carefully lays the foundations, and also develops the more advanced topics. ... This book gives a streamlined introduction for researchers and graduate students who want to apply these methods to other areas, and it would probably also provide a valuable reference source for researchers in the field. (Anton Deitmar, Bulletin of the London Mathematical Society, Vol. 34, 2002) The present book is a self-contained text which leads the reader through all the important aspects of the theory of locally convex vector spaces over nonarchimedean fields. ... The book gives a concise and clear account of this theory, it carefully lays the foundations and also develops the more advanced topics. Although the book will be a valuable reference work for experts in the field, it is mainly intended as streamlined but detailed introduction for researchers and graduate students ... . (L'Enseignement Mathematique, Vol. 48 (1-2), 2002)

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