Hypercyclicity of operators that λ-commute with the Hardy backward shift

2023/07/05 by Amouch, Mohamed, León-Saavedra, Fernando, de la Rosa, M. P. Romero
#37B20 #47A16 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2307.02271

Abstract

An operator T acting on a separable complex Hilbert space H is said to be hypercyclic if there exists f∈ H such that the orbit \Tⁿ f: n∈ ℕ\ is dense in H. Godefroy and Shapiro \citeGoSha characterized those elements in the commutant of the Hardy backward shift which are hypercyclic. In this paper we study some dynamics properties of operators X that λ-commute with the Hardy backward shift B, that is, BX=λXB.

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