Geodesic
Some versions of supercyclicity for a set of operators
Filomat, Tome 35 (2021) no. 5, p. 1619

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DOI

Let X be a complex topological vector space and L(X) the set of all continuous linear operators on X. An operator T ∈ L(X) is supercyclic if there is x ∈ X such that; COrb(T, x) = {αT n x : α ∈ C, n ≥ 0}, is dense in X. In this paper, we extend this notion from a single operator T ∈ L(X) to a subset of operators Γ ⊆ L(X). We prove that most of related proprieties to supercyclicity in the case of a single operator T remains true for subset of operators Γ. This leads us to obtain some results for C-regularized groups of operators.
DOI : 10.2298/FIL2105619A
Classification : 47A16
Keywords: Hypercyclicity, supercyclicity, orbit under a set, C-regularized group 
Mohamed Amouch; Otmane Benchiheb. Some versions of supercyclicity for a set of operators. Filomat, Tome 35 (2021) no. 5, p. 1619 . doi: 10.2298/FIL2105619A
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     title = {Some versions of supercyclicity for a set of operators},
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     doi = {10.2298/FIL2105619A},
     language = {en},
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