Some Properties and Criteria for Sub-Chaotic C₀-Semigroups

Mansooreh Moosapoor ⁽¹⁾ and Ismail Nikoufar ⁽²⁾

(1) Assistant Professor, Department of Mathematics, Farhangian University, P.O. Box 19989-63341, Tehran, Iran

Email address: m.mosapour@cfu.ac.ir

(2) Associate Professor, Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

Email address: nikoufar@pnu.ac.ir

Doi : https://doi.org/10.47013/15.4.18

Cited by : Jordan J. Math & Stat., 15 (4B) (2022), 1065 - 1076

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 Abstract. In this paper, we get a closer view to sub-chaotic C₀-semigroups. We show that if a C₀-semigroup contains a subspace-chaotic operator, then it is sub-chaotic. We prove that there are sub-chaotic C₀-semigroups that contain no subspace-chaotic operator. We also prove that if φ is a bounded and holomorphic function on the unit disk, then the multiplication C₀-semigroup generated by φ can not be sub-chaotic. Moreover, we state some criteria for a C₀-semigroup to be sub-chaotic based on the properties of the operators that made the semigroup.

Keywords: chaotic C₀-semigroups, sub-chaotic C₀-semigroups, subspace-chaotic operators, semigroups.