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Algebraic Multiplicity of Eigenvalues of Linear Operators

Algebraic Multiplicity of Eigenvalues of Linear Operators

Hardcover

Series: Operator Theory: Advances and Applications, Book 177

General MathematicsPhysics

ISBN10: 376438400X
ISBN13: 9783764384005
Publisher: Springer Nature
Published: Jun 22 2007
Pages: 310
Weight: 1.62
Height: 0.75 Width: 6.69 Depth: 9.61
Language: English
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.

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