On multiplicative perturbation of integral resolvent families

In this paper we study multiplicative perturbations for the generator of a strongly continuous integral resolvent family of bounded linear operators defined on a Banach space X. Assuming that a ( t ) is a creep function which satisfies a ( 0 + ) > 0 , we prove that if ( A , a ) generates an integ...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2007-03, Vol.327 (2), p.1335-1359
Main Authors: Lizama, Carlos, Poblete, Verónica
Format: Article
Language:English
Subjects:
Exact sciences and technology
Favard spaces
Functional analysis
Integral resolvent families
Mathematical analysis
Mathematics
Multiplicative perturbation
Operator theory
Resolvent families
Sciences and techniques of general use
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Summary:In this paper we study multiplicative perturbations for the generator of a strongly continuous integral resolvent family of bounded linear operators defined on a Banach space X. Assuming that a ( t ) is a creep function which satisfies a ( 0 + ) > 0 , we prove that if ( A , a ) generates an integral resolvent, then ( A ( I + B ) , a ) also generates an integral resolvent for all B ∈ B ( X , Z ) , where Z belongs to a class of admissible Banach spaces. In special instances of a ( t ) the space Z is proved to be characterized by an extended class of Favard spaces.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2006.04.087