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The Quarterly Journal of Mathematics Advance Access originally published online on December 4, 2007
The Quarterly Journal of Mathematics 2008 59(3):321-334; doi:10.1093/qmath/ham050
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© 2007. Published by Oxford University Press. All rights reserved For permissions, please email: journals.permissions@oxfordjournals.org

POWERS OF OPERATORS DOMINATED BY STRICTLY SINGULAR OPERATORS

Julio Flores{dagger}

Department of Applied Mathematics, Escet, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain

Francisco L. Hernández {ddagger} and Pedro Tradacete §

Departamento de Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid, Spain

{dagger} Corresponding author. E-mail: julio.flores{at}urjc.es

Received 22 June 2007; revised 24 September 2007
  Abstract

It is proved that every positive operator R on a Banach lattice E dominated by a strictly singular operator T:E -> E satisfies that the R4 is strictly singular. Moreover, if E is order continuous then the R2 is already strictly singular.

{ddagger} E-mail: pacoh{at}mat.ucm.es

§ E-mail: tradacete{at}mat.ucm.es


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