Some versions of supercyclicity for a set of operators | Zendy

Mohamed Amouch | Zendy; Otmane Benchihe | Zendy

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Some versions of supercyclicity for a set of operators

Author(s) -

Mohamed Amouch,

Otmane Benchihe

Publication year - 2021

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil2105619a

Subject(s) - mathematics , operator (biology) , set (abstract data type) , linear operators , discrete mathematics , pure mathematics , algebra over a field , combinatorics , mathematical analysis , computer science , biochemistry , chemistry , repressor , transcription factor , bounded function , gene , programming language

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) = {?Tnx : ? ? 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 ? ? 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 ?. This leads us to obtain some results for C-regularized groups of operators.

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