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J-Class Weighted Backward Shifts

    https://doi.org/10.1142/S0218127418500761Cited by:7 (Source: Crossref)

    In this article J-class operators are introduced and some basic properties of J-vectors are given. The J-class operators include the J-class operators and Jmix-class operators introduced by Costakis and Manoussos in 2008. This class also includes the Jwmix-class and Jerg-class operators defined by Zhang [2012]. Furthermore, for the unilateral weighted backward shifts on a Fréchet sequence space, we establish a criterion under which the shift operators belong to the J-class. From the criterion it is easy to obtain the existing criteria of hypercyclic backward shifts and of the topological mixing backward shifts. The obtained criterion also reveals the characteristic of J-class shift operators by the recurrence property. Meanwhile, we obtain infinite topological entropy when the shifts have stronger recurrence property, which generalizes the related results by Brian et al. in 2017.

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