English

Commutators on $L_p$, $1\le p<\infty$

Functional Analysis 2011-02-02 v1

Abstract

The operators on \LP=Lp[0,1]\LP=L_p[0,1], 1p<1\leq p<\infty, which are not commutators are those of the form λI+S\lambda I + S where λ0\lambda\neq 0 and SS belongs to the largest ideal in \opLP\opLP. The proof involves new structural results for operators on \LP\LP which are of independent interest.

Keywords

Cite

@article{arxiv.1102.0137,
  title  = {Commutators on $L_p$, $1\le p<\infty$},
  author = {Detelin Dosev and William B. Johnson and Gideon Schechtman},
  journal= {arXiv preprint arXiv:1102.0137},
  year   = {2011}
}
R2 v1 2026-06-21T17:19:54.899Z