The Kalton centralizer on $L_p[0,1]$ is not strictly singular
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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.References
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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
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 3447-3451
- MSC (2010): Primary 46B20, 46B07, 46A16
- DOI: https://doi.org/10.1090/S0002-9939-2013-11599-6
- MathSciNet review: 3080167