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Hypercyclic bilinear operators on Banach spaces (1905.12057v2)
Published 28 May 2019 in math.FA, math.CV, and math.DS
Abstract: We study the dynamics induced by an $m$-linear operator. We answer a question of B`es and Conejero showing an example of an $m$-linear hypercyclic operator acting on a Banach space. Moreover we prove the existence of $m$-linear hypercyclic operators on arbitrary infinite dimensional separable Banach spaces. We also prove an existence result about symmetric bihypercyclic bilinear operators, answering a question by Grosse-Erdman and Kim.