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Chain-finite operators and locally chain-finite operators

Published online by Cambridge University Press:  04 June 2001

Teresa Bermúdez  and
Antonio Martinón
Teresa Bermúdez
Affiliation:
Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain e-mail:[email protected], [email protected]
Antonio Martinón
Affiliation:
Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain e-mail:[email protected], [email protected]
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We give algebraic conditions characterizing chain-finite operators and locally chain-finite operators on Banach spaces. For instance, it is shown that T is a chain-finite operator if and only if some power of T is relatively regular and commutes with some generalized inverse; that is there are a bounded linear operator B and a positive integer k such that

TkBTk =Tk and TkB=BTk.

Moreover, we obtain an algebraic characterization of locally chain-finite operators similar to (1).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 43 , Issue 1 , January 2001 , pp. 113 - 121
Copyright
2001 Glasgow Mathematical Journal Trust