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© 2013

Representations of Linear Operators Between Banach Spaces

Benefits

  • No similar treatment existing in book form

  • Very recent and ongoing developments

  • Likely to stimulate interest in a difficult and interesting branch of analysis ?

Book

Part of the Operator Theory: Advances and Applications book series (OT, volume 238)

Table of contents

  1. Front Matter
    Pages i-xi
  2. David E. Edmunds, W. Desmond Evans
    Pages 1-66
  3. David E. Edmunds, W. Desmond Evans
    Pages 67-126
  4. David E. Edmunds, W. Desmond Evans
    Pages 127-140
  5. Back Matter
    Pages 141-152

About this book

Introduction

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.

Keywords

approximation property compact operators p-Laplacian strictly and unformly convex Banach spaces

Authors and affiliations

  1. 1.Department of MathematicsUniversity of SussexBrightonUnited Kingdom
  2. 2.School of MathematicsUniversity of CardiffCardiffUnited Kingdom

Bibliographic information

  • Book Title Representations of Linear Operators Between Banach Spaces
  • Authors David E. Edmunds
    W. Desmond Evans
  • Series Title Operator Theory: Advances and Applications
  • Series Abbreviated Title Operator Theory (Birkhäuser)
  • DOI https://doi.org/10.1007/978-3-0348-0642-8
  • Copyright Information Springer Basel 2013
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-0348-0641-1
  • eBook ISBN 978-3-0348-0642-8
  • Series ISSN 0255-0156
  • Series E-ISSN 2296-4878
  • Edition Number 1
  • Number of Pages XI, 152
  • Number of Illustrations 0 b/w illustrations, 1 illustrations in colour
  • Topics Operator Theory
    Partial Differential Equations
  • Buy this book on publisher's site

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)