In this paper, weighted backward shift operators $T_{\mathbf{w}}$ associated to a Schauder basis of a Banach space are considered. These operators are emblematic in the setting of linear chaos in topological vector spaces. In a constructive way, it is shown the existence of a dense linear subspace having maximal dimension, all of whose nonzero members are simultaneously $T_{\mathbf{w}}$-hypercyclic for every w belonging to a sequence of admissible weights. Our proof does not use any general result about algebraic or topological genericity.

中文翻译：

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Rolewicz算子的密集最大维超环子空间的构建

在本文中，加权后移算子${吨}_{\mathbf{w}}$考虑关联到 Banach 空间的 Schauder 基。这些算子在拓扑向量空间中的线性混沌设置中具有象征意义。以一种建设性的方式，它表明存在具有最大维度的密集线性子空间，其所有非零成员同时${吨}_{\mathbf{w}}$- 超循环对于属于一系列可接受权重的每个w 。我们的证明没有使用任何关于代数或拓扑通用性的一般结果。