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
DOI:
https://doi.org/10.1090/S0894-0347-2012-00748-6
Published electronically:
August 21, 2012
MathSciNet review:
2983007
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
Article copyright:
© Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
