Commutators on 𝐿_{𝑝}, 1≤𝑝<∞

Dosev, Detelin; Johnson, William; Schechtman, Gideon

doi:10.1090/S0894-0347-2012-00748-6

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

Authors: Detelin Dosev, William B. Johnson and Gideon Schechtman
Journal: J. Amer. Math. Soc. 26 (2013), 101-127
MSC (2010): Primary 47B47; Secondary 46E30
DOI: https://doi.org/10.1090/S0894-0347-2012-00748-6
Published electronically: August 21, 2012
MathSciNet review: 2983007
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Abstract: The operators on , $1\leq p<\infty$ , which are not commutators are those of the form $\lambda I + S$ , where $\lambda \neq 0$ and belongs to the largest ideal in $\mathcal {L}(L_p)$ . The proof involves new structural results for operators on 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: https://doi.org/10.1090/S0894-0347-2012-00748-6
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.