Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
23 January 2020 |
07 February 2020 |
10 March 2020 |
Abstract: Let X be a Banach space with dim X>1 such that its topological dual X* is separable and B(X) the algebra of all bounded linear operators on X. In the present work, we introduce the concept of mixing recurrent and we investigate the study of recurrent and mixing recurrent for elementary operators on an admissible Banach ideal (J, ||.||J) of B(X). Also, we study the passage of property of being supercyclic from an operator T∊B(X) to the left and the right multiplication LT and RT induced by T on (J, ||.||J). In particular, we prove that : 1) T satisfies the supercyclicity criterion on X if and only if LT is supercyclic on (J, ||.||J). 2) T* satisfies the supercyclicity criterion on X* if and only if RT is supercyclic on (J, ||.||J). 3) T⨁T is recurrent on X⨁X if and only if LT is recurrent on (J, ||.||J). 4) T is mixing recurrent on X if and only if LT is mixing recurrent on (J, ||.||J).
