
Algebraic Multiplicity of Eigenvalues of Linear Operators
Birkhäuser (Publisher)
Published on 22. June 2007
Book
Hardback
XXII, 310 pages
978-3-7643-8400-5 (ISBN)
Description
This book analyzes the existence and uniqueness of a generalized algebraic m- tiplicity for a general one-parameter family L of bounded linear operators with Fredholm index zero at a value of the parameter ? whereL(? ) is non-invertible. 0 0 Precisely, given K?{R,C}, two Banach spaces U and V over K, an open subset ? ? K,andapoint ? ? ?, our admissible operator families are the maps 0 r L?C (? ,L(U,V)) (1) for some r? N, such that L(? )? Fred (U,V); 0 0 hereL(U,V) stands for the space of linear continuous operatorsfrom U to V,and Fred (U,V) is its subset consisting of all Fredholm operators of index zero. From 0 the point of view of its novelty, the main achievements of this book are reached in case K = R, since in the case K = C and r = 1, most of its contents are classic, except for the axiomatization theorem of the multiplicity.
More details
Series
Edition
2007 ed.
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
XXII, 310 p.
Dimensions
Height: 250 mm
Width: 175 mm
Thickness: 24 mm
Weight
762 gr
ISBN-13
978-3-7643-8400-5 (9783764384005)
DOI
10.1007/978-3-7643-8401-2
Schweitzer Classification
Other editions
Additional editions

Julián López-Gómez | Carlos Mora-Corral
Algebraic Multiplicity of Eigenvalues of Linear Operators
E-Book
08/2007
1st Edition
Birkhäuser
€96.29
Available for download
Content
Finite-dimensional Classic Spectral Theory.- The Jordan Theorem.- Operator Calculus.- Spectral Projections.- Algebraic Multiplicities.- Algebraic Multiplicity Through Transversalization.- Algebraic Multiplicity Through Polynomial Factorization.- Uniqueness of the Algebraic Multiplicity.- Algebraic Multiplicity Through Jordan Chains. Smith Form.- Analytic and Classical Families. Stability.- Algebraic Multiplicity Through Logarithmic Residues.- The Spectral Theorem for Matrix Polynomials.- Further Developments of the Algebraic Multiplicity.- Nonlinear Spectral Theory.- Nonlinear Eigenvalues.