Representation of commutators on Schatten p-classes

被引：0
|
作者：
Cheng, Lixin [1 ]
Yu, Zhizheng [1 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China
来源：
JOURNAL OF NONCOMMUTATIVE GEOMETRY | 2024年 / 18卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Commutator; Schatten-p class; strictly singular operator; maximal ideal; Banach space; SUBSPACES; SPACES;
D O I：
10.4171/7NCG/542
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let Cp be the Schatten p -class of t2 for 1 < p < infinity, and let Tp be the closed subspace of Cp consisting of all lower triangular matrices. In this paper, we show that a bounded linear operator T on Cp is a commutator if and only if T is not of the form AI + K, where 0 # A E C and K is a Cp-strictly singular operator. It is done by showing that a bounded linear operator T on T-p is not a commutator if and only if T has the same form.
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页码：741 / 770
页数：30
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