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Norms of basic elementary operators on algebras of regular operators


Author: A. W. Wickstead
Journal: Proc. Amer. Math. Soc. 143 (2015), 5275-5280
MSC (2010): Primary 47B48, 47B60
DOI: https://doi.org/10.1090/proc/12664
Published electronically: May 22, 2015
MathSciNet review: 3411145
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Abstract: We show that if $ E$ is an atomic Banach lattice with an order continuous norm, $ A,B\in \mathcal {L}^r(E)$ and $ M_{A,B}$ is the operator on $ \mathcal {L}^r(E)$ defined by $ M_{A,B}(T)=ATB$, then $ \Vert M_{A,B}\Vert _r=\Vert A\Vert _r\Vert B\Vert _r$ but that there is no real $ \alpha >0$ such that $ \Vert M_{A,B}\Vert\ge \alpha \Vert A\Vert _r\Vert B\Vert _r$.


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Additional Information

A. W. Wickstead
Affiliation: Pure Mathematics Research Centre, Queen’s University Belfast, Belfast BT7 1NN, Northern Ireland
Email: A.Wickstead@qub.ac.uk

DOI: https://doi.org/10.1090/proc/12664
Keywords: Regular operators, basic elementary operators, Banach lattices
Received by editor(s): March 26, 2014
Received by editor(s) in revised form: May 6, 2014, and September 18, 2014
Published electronically: May 22, 2015
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2015 American Mathematical Society