We study the existence of algebras of hypercyclic vectors for weighted backward shifts on Fr\'echet sequence spaces that are algebras when endowed with coordinatewise multiplication or with the Cauchy product. As a particular case we obtain that the sets of hypercyclic vectors for Rolewicz's and MacLane's operators are algebrable.

中文翻译：

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后移算子的超循环向量集的可代数性

我们研究了 Fr\'echet 序列空间上加权向后移位的超循环向量代数的存在，这些空间是具有坐标乘法或柯西乘积的代数。作为一个特殊情况，我们获得了 Rolewicz 和 MacLane 算子的超循环向量集是可代数的。