Representation of commutators on Schatten -classes
Lixin Cheng
Xiamen University, ChinaZhizheng Yu
Xiamen University, China
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Abstract
Let be the Schatten -class of for , and let be the closed subspace of consisting of all lower triangular matrices. In this paper, we show that a bounded linear operator on is a commutator if and only if is not of the form , where and is a -strictly singular operator. It is done by showing that a bounded linear operator on is not a commutator if and only if has the same form.
Cite this article
Lixin Cheng, Zhizheng Yu, Representation of commutators on Schatten -classes. J. Noncommut. Geom. 18 (2024), no. 2, pp. 741–770
DOI 10.4171/JNCG/542