{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T04:24:37Z","timestamp":1769228677374,"version":"3.49.0"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2018,6,15]]},"abstract":"<jats:p> In this article [Formula: see text]-class operators are introduced and some basic properties of [Formula: see text]-vectors are given. The [Formula: see text]-class operators include the [Formula: see text]-class operators and [Formula: see text]-class operators introduced by Costakis and Manoussos in 2008. This class also includes the [Formula: see text]-class and [Formula: see text]-class operators defined by Zhang [2012]. Furthermore, for the unilateral weighted backward shifts on a Fr\u00e9chet sequence space, we establish a criterion under which the shift operators belong to the [Formula: see text]-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 [Formula: see text]-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. <\/jats:p>","DOI":"10.1142\/s0218127418500761","type":"journal-article","created":{"date-parts":[[2018,6,21]],"date-time":"2018-06-21T03:03:03Z","timestamp":1529550183000},"page":"1850076","source":"Crossref","is-referenced-by-count":9,"title":["J\u2131-Class Weighted Backward Shifts"],"prefix":"10.1142","volume":"28","author":[{"given":"Shengnan","family":"He","sequence":"first","affiliation":[{"name":"School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. 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