This is an announcement for the paper "Commutators on $\ell_1$" by Detelin Dosev.

Abstract: The main result is that the commutators on $\ell_1$ are the operators not of the form $\lambda I + K$ with $\lambda\neq 0$ and $K$ compact. We generalize Apostol's technique (1972, Rev. Roum. Math. Appl. 17) to obtain this result and use this generalization to obtain partial results about the commutators on spaces $\X$ which can be represented as $\displaystyle \X\simeq \left ( \bigoplus_{i=0}^{\infty} \X\right)_{p}$ for some $1\leq p<\infty$ or $p=0$. In particular, it is shown that every compact operator on $L_1$ is a commutator. A characterization of the commutators on $\ell_{p_1}\oplus\ell_{p_2}\oplus\cdots\oplus\ell_{p_n}$ is given. We also show that strictly singular operators on $\linf$ are commutators.

Archive classification: math.FA

Mathematics Subject Classification: 47B47

Remarks: 17 pages. Submitted to the Journal of Functional Analysis

The source file(s), Commutators_l1.tex: 58728 bytes, is(are) stored in gzipped form as 0809.3047.gz with size 16kb. The corresponding postcript file has gzipped size 110kb.

Submitted from: ddosev@gmail.com

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