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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Kalton centralizer on $ L_p[0,1]$ is not strictly singular


Author: Jesús Suárez de la Fuente
Journal: Proc. Amer. Math. Soc. 141 (2013), 3447-3451
MSC (2010): Primary 46B20, 46B07, 46A16
Published electronically: June 5, 2013
MathSciNet review: 3080167
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Abstract: We prove that the Kalton centralizer on $ L_p[0,1]$, for $ 0<p<\infty $, is not strictly singular: in all cases there is a Hilbert subspace on which it is trivial. Moreover, for $ 0<p<2$ there are copies of $ \ell _q$, with $ p<q<2$, on which it becomes trivial. This is in contrast to the situation for $ \ell _p$ spaces, in which the Kalton-Peck centralizer is strictly singular.


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Additional Information

Jesús Suárez de la Fuente
Affiliation: Escuela Politécnica, Universidad de Extremadura, Avenida Universidad s/n, 10071 Cáceres, Spain
Email: jesus@unex.es

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11599-6
PII: S 0002-9939(2013)11599-6
Received by editor(s): March 31, 2011
Received by editor(s) in revised form: October 20, 2011, October 24, 2011, November 16, 2011, and December 8, 2011
Published electronically: June 5, 2013
Additional Notes: The author was partially supported by MTM2010-20190-C02-01 and Junta de Extremadura CR10113 “IV Plan Regional I+D+i”, Ayudas a Grupos de Investigación
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.