Skip Navigation

Journal of the London Mathematical Society 2004 69(1):231-242; doi:10.1112/S002461070300471X
© 2004 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Mora-Corral, C.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The London Mathematical Society

On the Uniqueness of the Algebraic Multiplicity

C. Mora-Corral

Departamento de Matemática Aplicada, Universidad Complutense de Madrid 28040-Madrid, Spain, carlos_mora{at}mat.ucm.es

Received 31 January 2003. Revision received 14 May 2003.

Given a smooth family £ of real or complex variable taking values within the class of Fredholm operators of index zero in a Banach space, there are some available definitions in the literature of the concept of algebraic multiplicity of the family £ at a point x0 of the parameter at which the operator L(x0) becomes non-invertible. The purpose of the paper is to show that the algebraic multiplicity is uniquely determined by a few of its properties, independently of its construction. The main technical tools to obtain this uniqueness result are a Lyapunov–Schmidt reduction, the local Smith form and a new factorization result for general families at non-algebraic eigenvalues obtained in the paper.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.