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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Commutators on $ L_p$, $ 1{\leq}p <\infty$


Authors: Detelin Dosev, William B. Johnson and Gideon Schechtman
Journal: J. Amer. Math. Soc. 26 (2013), 101-127
MSC (2010): Primary 47B47; Secondary 46E30
Published electronically: August 21, 2012
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Abstract: The operators on $ L_p=L_p[0,1]$, $ 1\leq p<\infty $, which are not commutators are those of the form $ \lambda I + S$, where $ \lambda \neq 0$ and $ S$ belongs to the largest ideal in $ \mathcal {L}(L_p)$. The proof involves new structural results for operators on $ L_p$ which are of independent interest.


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Additional Information

Detelin Dosev
Affiliation: Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel
Email: dosevd@weizmann.ac.il

William B. Johnson
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: johnson@math.tamu.edu

Gideon Schechtman
Affiliation: Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel
Email: gideon@weizmann.ac.il

DOI: http://dx.doi.org/10.1090/S0894-0347-2012-00748-6
PII: S 0894-0347(2012)00748-6
Received by editor(s): February 2, 2011
Received by editor(s) in revised form: May 30, 2012
Published electronically: August 21, 2012
Additional Notes: The first author was Young Investigator, NSF Workshop in Analysis and Probability, Texas A&M University
The second author was supported in part by NSF DMS-1001321 and U.S.-Israel Binational Science Foundation
The third author was supported in part by U.S.-Israel Binational Science Foundation. Participant NSF Workshop in Analysis and Probability, Texas A&M University
Dedicated: Dedicated to the memory of Nigel Kalton
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.