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Ideals of operators on $(\oplus \ell ^\infty (n))_{\ell ^1}$


Author: Denny H. Leung
Journal: Proc. Amer. Math. Soc. 143 (2015), 3047-3053
MSC (2010): Primary 47L10; Secondary 46H10
DOI: https://doi.org/10.1090/S0002-9939-2015-12500-2
Published electronically: February 20, 2015
MathSciNet review: 3336629
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Abstract: The unique maximal ideal in the Banach algebra $L(E)$, $E = (\oplus \ell ^\infty (n))_{\ell ^1}$, is identified. The proof relies on techniques developed by Laustsen, Loy and Read (published in the Journal of Functional Analysis in 2004) and a dichotomy result for operators mapping into $L^1$ due to Laustsen, Odell, Schlumprecht and Zsák (published in the Journal of the London Mathematical Society in 2012).


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Additional Information

Denny H. Leung
Affiliation: Department of Mathematics, National University of Singapore, Singapore 119076
MR Author ID: 113100
Email: matlhh@nus.edu.sg

Received by editor(s): October 28, 2013
Received by editor(s) in revised form: March 17, 2014
Published electronically: February 20, 2015
Additional Notes: This research was partially supported by Academic Research Fund project no. R-146-000-157-112
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2015 American Mathematical Society