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：

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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。