Abstract
We explore the hypercyclicity of unilateral weighted backward shifts and bilateral weighted shifts on \(\ell ^p\), where \(1\le p \le \infty \), with the weak or weak-star topologies. Then, we turn our attention to see how a nonzero limit point of an orbit of such an operator determines the hypercyclicity of the operator. Lastly, we explore a recent result that a unilateral weighted backward shift can be factored as the product of two hypercyclic shifts.
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Chan, K.C. (2021). The Testing Ground of Weighted Shift Operators for Hypercyclicity. In: Devaney, R.L., Chan, K.C., Vinod Kumar, P. (eds) Topological Dynamics and Topological Data Analysis. IWCTA 2018. Springer Proceedings in Mathematics & Statistics, vol 350. Springer, Singapore. https://doi.org/10.1007/978-981-16-0174-3_10
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DOI: https://doi.org/10.1007/978-981-16-0174-3_10
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