Representations of Linear Operators Between Banach Spaces

Representations of Linear Operators Between Banach Spaces

Hardback Operator Theory: Advances and Applications

By (author) David Eric Edmunds, By (author) William D. Evans

$101.63
List price $119.50
You save $17.87 14% off

Free delivery worldwide
Available
Dispatched in 4 business days
When will my order arrive?

  • Publisher: Springer Basel
  • Format: Hardback | 163 pages
  • Dimensions: 155mm x 234mm x 15mm | 363g
  • Publication date: 13 September 2013
  • ISBN 10: 3034806418
  • ISBN 13: 9783034806411
  • Edition statement: 2013 ed.
  • Illustrations note: 1 colour illustrations, biography
  • Sales rank: 1,902,353

Product description

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.

Other people who viewed this bought:

Showing items 1 to 10 of 10

Other books in this category

Showing items 1 to 11 of 11
Categories:

Review quote

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)

Back cover copy

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.

Table of contents

1 Preliminaries.- 2 Representation of compact linear operators.- 3 Representation of bounded linear operators.