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Nonarchimedean Functional Analysis (Springer Monographs in Mathematics) - Hardcover

Buch 13 von 187: Springer Monographs in Mathematics

Schneider, Peter

 
9783540425335: Nonarchimedean Functional Analysis (Springer Monographs in Mathematics)
Hardcover
ISBN 10: 3540425330 ISBN 13: 9783540425335
Verlag: Springer, 2001

Inhaltsangabe

This book grew out of a course which I gave during the winter term 1997/98 at the Universitat Munster. The course covered the material which here is presented in the first three chapters. The fourth more advanced chapter was added to give the reader a rather complete tour through all the important aspects of the theory of locally convex vector spaces over nonarchimedean fields. There is one serious restriction, though, which seemed inevitable to me in the interest of a clear presentation. In its deeper aspects the theory depends very much on the field being spherically complete or not. To give a drastic example, if the field is not spherically complete then there exist nonzero locally convex vector spaces which do not have a single nonzero continuous linear form. Although much progress has been made to overcome this problem a really nice and complete theory which to a large extent is analogous to classical functional analysis can only exist over spherically complete field8. I therefore allowed myself to restrict to this case whenever a conceptual clarity resulted. Although I hope that thi8 text will also be useful to the experts as a reference my own motivation for giving that course and writing this book was different. I had the reader in mind who wants to use locally convex vector spaces in the applications and needs a text to quickly gra8p this theory.

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Über die Autorin bzw. den Autor

Peter Schneider is a Full Professor for Astrophysics at the University of Bonn and Founding Director of the Argelander-Institut für Astronomie, Bonn. He is one of the internationally most respected German astrophysicists, well known for his research on gravitational lensing (strong and weak) and cosmology, and author of 3 successful Springer books.

Von der hinteren Coverseite

This book grew out of a course which I gave during the winter term 1997/98 at the Universitat Munster. The course covered the material which here is presented in the first three chapters. The fourth more advanced chapter was added to give the reader a rather complete tour through all the important aspects of the theory of locally convex vector spaces over nonarchimedean fields. There is one serious restriction, though, which seemed inevitable to me in the interest of a clear presentation. In its deeper aspects the theory depends very much on the field being spherically complete or not. To give a drastic example, if the field is not spherically complete then there exist nonzero locally convex vector spaces which do not have a single nonzero continuous linear form. Although much progress has been made to overcome this problem a really nice and complete theory which to a large extent is analogous to classical functional analysis can only exist over spherically complete field8. I therefore allowed myself to restrict to this case whenever a conceptual clarity resulted. Although I hope that thi8 text will also be useful to the experts as a reference my own motivation for giving that course and writing this book was different. I had the reader in mind who wants to use locally convex vector spaces in the applications and needs a text to quickly gra8p this theory.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Springer
Erscheinungsdatum
2001
Sprache
Englisch
ISBN 10 
3540425330
ISBN 13 
9783540425335
Einband
Gebundene Ausgabe
Anzahl der Seiten
163
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