Multiplication operators between discrete Hardy spaces on rooted trees

Abstract: Muthukumar and Ponnusamy \cite{MP-Tp-spaces} studied the multiplication operators on $\mathbb{T}p$ spaces. In this article, we mainly consider multiplication operators between $\mathbb{T}_p$ and $\mathbb{T}_q$ ($p\neq q$). In particular, we characterize bounded and compact multiplication operators from $\mathbb{T}{p}$ to $\mathbb{T}{q}$. For $p\neq q$, we prove that there are no invertible multiplication operators from $\mathbb{T}{p}$ to $\mathbb{T}{q}$ and also there are no isometric multiplication operators from $\mathbb{T}{p}$ to $\mathbb{T}{q}$. Finally, we discuss about fixed points of a multiplication operator on $\mathbb{T}{p}$.