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Linear relations on hereditarily indecomposable normed spaces

Published online by Cambridge University Press:  17 April 2009

Teresa Álvarez
Teresa Álvarez
Affiliation:
Department of Mathematics, University of Oviedo, 33007, Oviedo, Asturias, Spain e-mail: seco@uniovi.es
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We introduce the notion of hereditarily indecomposable normed space and we prove that this class of normed spaces may be characterised by means of F+ and strictly singular linear relations. We also show that if X is a complex hereditarily indecomposable normed space then every partially continuous linear relation in X with dense domain can be written as λI + S, where λ ∈ ℂ and S is a strictly singular linear relation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 74 , Issue 2 , October 2006 , pp. 289 - 300
Copyright
Copyright © Australian Mathematical Society 2006

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