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

## TL;DR

This paper investigates how supercyclicity properties of operators on Banach spaces transfer to their induced left and right multiplication operators on Banach ideals, providing conditions for supercyclicity and criteria equivalences.

## Contribution

It introduces sufficient conditions for supercyclicity transfer from operators to their induced multiplication operators on Banach ideals and offers new equivalent conditions for the Supercyclicity Criterion.

## Key findings

- Supercyclicity can transfer from an operator to its induced multiplication operators under certain conditions.
- A sufficient condition for the tensor product of two operators to be supercyclic is established.
- New equivalent conditions for the Supercyclicity Criterion are provided.

## 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.