Operator Theory: Advances and Applications

Representations of Linear Operators Between Banach Spaces

Authors: Edmunds, David E., Evans, W. Desmond

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  • Very recent and ongoing developments
  • Likely to stimulate interest in a difficult and interesting branch of analysis ​
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About this book

The book deals with the representation in series form of compact linear operators acting between Banach spaces, and provides an analogue of the classical Hilbert space results of this nature that have their roots in the work of D. Hilbert, F. Riesz and E. Schmidt. The representation involves a recursively obtained sequence of points on the unit sphere of the initial space and a corresponding sequence of positive numbers that correspond to the eigenvectors and eigenvalues of the map in the Hilbert space case. The lack of orthogonality is partially compensated by the systematic use of polar sets. There are applications to the p-Laplacian and similar nonlinear partial differential equations. Preliminary material is presented in the first chapter, the main results being established in Chapter 2. The final chapter is devoted to the problems encountered when trying to represent non-compact maps.

Reviews

From the reviews:

“Book presents an account of the spectral theory of operators acting in Banach spaces. … notes and comments at the end of each chapter give a fairly complete documentation, enabling the reader to trace the material to its sources, pursue the topics further and see them in context. As an authoritative account of a new and rapidly developing branch of spectral theory, this work will be of great interest to research workers and students in the field and related topics.” (Petru A. Cojuhari, zbMATH, Vol. 1283, 2014)


Table of contents (3 chapters)

  • Preliminaries

    Edmunds, David E. (et al.)

    Pages 1-66

  • Representation of Compact Linear Operators

    Edmunds, David E. (et al.)

    Pages 67-126

  • Representation of Bounded Linear Operators

    Edmunds, David E. (et al.)

    Pages 127-140

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-0348-0642-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-0348-0641-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Representations of Linear Operators Between Banach Spaces
Authors
Series Title
Operator Theory: Advances and Applications
Series Volume
238
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0642-8
DOI
10.1007/978-3-0348-0642-8
Hardcover ISBN
978-3-0348-0641-1
Series ISSN
0255-0156
Edition Number
1
Number of Pages
XI, 152
Number of Illustrations and Tables
1 illustrations in colour
Topics