Abstract of a paper by Detelin Dosev
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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.3047 or http://arXiv.org/abs/0809.3047 or by email in unzipped form by transmitting an empty message with subject line uget 0809.3047 or in gzipped form by using subject line get 0809.3047 to: math@arXiv.org.
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alspach@fourier.math.okstate.edu