双边加权移位算子的超循环移位因子分解

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Operator Theory Pub Date : 2021-03-15 DOI:10.7900/jot.2019jul22.2284

Kit C. Chan, Rebecca Sanders

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引用次数: 1

摘要

从双边加权移位是一个算子的角度来看，它移位了ℓp（Z），在1⩽p<∞的情况下，我们证明了ℓp（Z）具有因子分解T=AB，其中a和B是超循环双边加权移位。对于T可逆的情况，移位A和移位B也可以被选择为可逆。此外，我们还给出了具有非零对角项的对角算子的类似超循环因子分解结果。

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Hypercyclic shift factorizations for bilateral weighted shift operators

Taking the perspective that a bilateral weighted shift is an operator that shifts some two-sided canonical basic sequence of ℓp(Z), with 1⩽p<∞, we show that every bilateral weighted shift on ℓp(Z) has a factorization T=AB, where A and B are hypercyclic bilateral weighted shifts. For the case when T is invertible, both shifts A and B may be selected to be invertible as well. Moreover, we show analogous hypercyclic factorization results for diagonal operators with nonzero diagonal entries.

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来源期刊

Journal of Operator Theory 数学-数学

CiteScore

1.30

自引率

12.50%

发文量

审稿时长

12 months

期刊介绍： The Journal of Operator Theory is rigorously peer reviewed and endevours to publish significant articles in all areas of operator theory, operator algebras and closely related domains.