## 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.## References

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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 - © 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

Dedicated: Dedicated to the memory of Nigel Kalton