
Representations of Linear Operators Between Banach Spaces
Birkhäuser (Publisher)
Published on 13. September 2013
Book
Hardback
XI, 152 pages
978-3-0348-0641-1 (ISBN)
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.
Reviews / Votes
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)
More details
Series
Edition
2013 ed.
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
1 farbige Abbildung
XI, 152 p. 1 illus. in color.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 14 mm
Weight
424 gr
ISBN-13
978-3-0348-0641-1 (9783034806411)
DOI
10.1007/978-3-0348-0642-8
Schweitzer Classification
Other editions
Additional editions

David E. Edmunds | W. Desmond Evans
Representations of Linear Operators Between Banach Spaces
E-Book
09/2013
1st Edition
Birkhäuser
€53.49
Available for download
Content
1 Preliminaries.- 2 Representation of compact linear operators.- 3 Representation of bounded linear operators.