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A Hausdorff Operator with Commuting Family of Perturbation Matrices Is a Non-Riesz Operator
Russian Journal of Mathematical Physics ( IF 1.7 ) Pub Date : 2020-12-22 , DOI: 10.1134/s1061920820040081 A. R. Mirotin
中文翻译:
具有通勤矩阵族的Hausdorff算子是非Riesz算子
更新日期:2020-12-23
Russian Journal of Mathematical Physics ( IF 1.7 ) Pub Date : 2020-12-22 , DOI: 10.1134/s1061920820040081 A. R. Mirotin
Abstract
We consider a generalization of the notion of Hausdorff operator on Lebesgue spaces and, under natural conditions, prove that such an operator is not a Riesz operator provided it is non zero. In particular, it cannot be represented as a sum of a quasinilpotent and a compact operators.
中文翻译:
具有通勤矩阵族的Hausdorff算子是非Riesz算子
摘要
我们考虑了Hausdorff算子在Lebesgue空间上的概化,并在自然条件下证明了该算子不是Riesz算子,只要它不是零。特别是,它不能表示为准幂和紧算子的总和。