Nonarchimedean Functional Analysis

Peter Schneider, geboren 1940 in Lübeck, ist in Süddeutschland aufgewachsen, studierte in Freiburg Germanistik und Geschichte und lebt seit 1961 als freier Schriftsteller. 1972 Staatsexamen, 1973 Berufsverbot als Referendar. Mehrere Förderpreise; 1977/78 Stipendium der Villa Massimo. Schneiders theoretische Schriften dokumentieren den Ablauf der Studentenrevolte der späten 60er Jahre, an der er in Berlin und Italien aktiv teilnahm. Diese Erfahrungen sowie das zeitweilige Berufsverbot bestimmen seine ersten Erzählungen. 2009 erhielt er den Schubart-Literaturpreis der Stadt Aalen.

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.

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." (Dinamérico 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)