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arXiv · 1905.04503

Supercyclicity of the left and right multiplication operators on Banach ideal of operators

Mohamed Amouch·Hamza Lakrimi
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Abstract

Let $X$ be a Banach space with $\dim X>1$ such that $X^{\ast}$, its dual, is separable and $\mathcal{B}(X)$ the algebra of bounded linear operators on $X$. In this paper, we study the passage of property of being supercyclic from an operator $T\in\mathcal{B}(X)$ to the left and right multiplication induced by $T$ on separable admissible Banach ideal of $\mathcal{B}(X)$. We give a sufficient condition for the tensor product $T\widehat{\otimes}R$ of two operators to be supercyclic. As a consequence, we give another equivalent conditions for the Supercyclicity Criterion.

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Mohamed Amouch, Hamza Lakrimi. 2019-05-11. Supercyclicity of the left and right multiplication operators on Banach ideal of operators. https://arxiv.org/abs/1905.04503

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