Laurent series for inversion of linearly perturbed bounded linear operators on Banach space

In this paper we find necessary and sufficient conditions for the existence of a Laurent series expansion with a finite order pole at the origin for the inverse of a linearly perturbed bounded linear operator mapping one Banach space to another. In particular we show that the inversion defines linea...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical analysis and applications 2010-06, Vol.366 (1), p.112-123
Main Authors: Howlett, Phil, Albrecht, Amie, Pearce, Charles
Format: Article
Language:English
Subjects:
Banach space
Bounded linear operators
Exact sciences and technology
Functional analysis
Functions of a complex variable
Laurent series
Linear perturbation
Mathematical analysis
Mathematics
Operator theory
Sciences and techniques of general use
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we find necessary and sufficient conditions for the existence of a Laurent series expansion with a finite order pole at the origin for the inverse of a linearly perturbed bounded linear operator mapping one Banach space to another. In particular we show that the inversion defines linear projections that separate the Banach spaces into corresponding complementary subspaces. We present two pertinent applications.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2009.12.007