Representations Of Linear Operators Between Banach Spaces
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Representations of Linear Operators Between Banach Spaces
Author: David E. Edmunds
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-09-04
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.
Spectral Theory of Linear Operators
General spectral theory; Riesz operators; Hermitian operators; Prespectral operators; Well-bounded operators.
History of Banach Spaces and Linear Operators
Author: Albrecht Pietsch
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-12-31
Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.