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SpringerBriefs in Mathematics

Non-Archimedean Operator Theory

Authors: Diagana, Toka, Ramaroson, François

  • Presents spectral theory in the non-Archimedean setting; useful to physicists and theoretically-oriented engineers
  • Details fundamental material which renders a useful reference for students and researchers
  • Useful for independent study or seminar use
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eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-27323-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-27322-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book  focuses on the theory of linear operators on non-Archimedean Banach spaces.  The topics treated in this book range from a basic introduction to non-Archimedean valued fields, free non-Archimedean Banach spaces, bounded and unbounded linear operators in the non-Archimedean setting, to the spectral theory for some classes of linear operators. The theory of Fredholm operators is emphasized and used  as an important tool in the study of the spectral theory of non-Archimedean operators. Explicit descriptions of the spectra of some operators are worked out. Moreover, detailed background materials on non-Archimedean valued fields and free non-Archimedean Banach spaces are included for completeness and for reference. 


The readership of the book is aimed toward graduate and postgraduate students, mathematicians, and non-mathematicians such as physicists and engineers who are interested in non-Archimedean functional analysis. Further, it can be used as an introduction to the study of non-Archimedean operator theory in general and to the study of spectral theory in other special cases. 

Reviews

“This book presents some of the authors’ recent work on continuous linear operators on non-archimedean Banach space as well as their spectral theory. … The book can be recommended to beginners as an introduction to non-archimendean operator theory.” (Bertin Diarra, Mathematical Reviews, January, 2017)

“The book is intended as an introduction to the non-Archimedean operator theory ‘for graduate and postgraduate students, mathematicians, and non-mathematicians such as physicists and engineers who are interested in functional analysis in the non-Archimedean context’. Of course, expecting the readership being so wide, the authors make the exposition as elementary as possible.” (Anatoly N. Kochubei, zbMATH 1357.47002, 2017)


Table of contents (7 chapters)

  • Non-Archimedean Valued Fields

    Diagana, Toka (et al.)

    Pages 1-39

  • Non-Archimedean Banach Spaces

    Diagana, Toka (et al.)

    Pages 41-60

  • Bounded Linear Operators in Non-Archimedean Banach Spaces

    Diagana, Toka (et al.)

    Pages 61-84

  • The Vishik Spectral Theorem

    Diagana, Toka (et al.)

    Pages 85-105

  • Spectral Theory for Perturbations of Bounded Diagonal Linear Operators

    Diagana, Toka (et al.)

    Pages 107-121

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-27323-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-27322-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Non-Archimedean Operator Theory
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-27323-5
DOI
10.1007/978-3-319-27323-5
Softcover ISBN
978-3-319-27322-8
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XIII, 156
Topics