Algebraic Multiplicity of Eigenvalues of Linear Operators

By J. Lopez-Gomez, Carlos Mora-Corral, J. Lopez-Gomez

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.

• Format: Hardcover
• Language: English
• ISBN: 376438400X
• ISBN13: 9783764384005
• Release Date: June 2007
• Publisher: Birkhauser
• Length: 310 Pages
• Weight: 1.62 lbs.
• Dimensions: 0.8" x 6.7" x 9.6"