Skip to main content
SpringerLink
Log in
Book cover
  • Book
  • © 2007

Algebraic Multiplicity of Eigenvalues of Linear Operators

Birkhäuser

Authors:

  1. J. López-Gómez

    1. Department of Applied Mathematics, Universidad Complutense de Madrid, Madrid, Spain

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. C. Mora-Corral

    1. Mathematical Institute, University of Oxford, Oxford, UK

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Introduces readers to the classic theory with the most modern terminology, and, simultaneously, conducts readers comfortably to the latest developments in the theory of the algebraic multiplicity of eigenvalues of one-parameter families of Fredholm operators of index zero
  • Gives a very comfortable access to the latest developments in the real non-analytic case, where optimal results are included by the first time in a monograph
  • Recent results presented include the uniqueness of the algebraic multiplicity, which has important implications
  • Includes supplementary material: sn.pub/extras

Part of the book series: Operator Theory: Advances and Applications (OT, volume 177)

  • 12k Accesses

Sections

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (12 chapters)

  1. Front Matter

    Pages i-xxii
    PDF

  2. Finite-dimensional Classic Spectral Theory

    1. Front Matter

      Pages 1-2
      PDF

    2. The Jordan Theorem

      Pages 3-35

    3. Operator Calculus

      Pages 37-62

    4. Spectral Projections

      Pages 63-73

  4. Nonlinear Spectral Theory

    1. Front Matter

      Pages 271-272
      PDF

    2. Nonlinear Eigenvalues

      Pages 273-293

  5. Back Matter

    Pages 295-310
    PDF
Back to top

About this book

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.
Back to top

Keywords

Back to top

Authors and Affiliations

  • Department of Applied Mathematics, Universidad Complutense de Madrid, Madrid, Spain

    J. López-Gómez

  • Mathematical Institute, University of Oxford, Oxford, UK

    C. Mora-Corral

Back to top

Bibliographic Information

Back to top

Publish with us

Policies and ethics

Back to top
Access via your institution

Search

Navigation