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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Commutators on $L_p$, $1\leq p <\infty$
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by Detelin Dosev, William B. Johnson and Gideon Schechtman PDF
J. Amer. Math. Soc. 26 (2013), 101-127 Request permission

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
  • MR Author ID: 95220
  • Email: johnson@math.tamu.edu
  • Gideon Schechtman
  • Affiliation: Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel
  • MR Author ID: 155695
  • Email: gideon@weizmann.ac.il
  • 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
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2983007