Multiplication operators between discrete Hardy spaces on rooted trees

P. Muthukumar; P. Shankar

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arXiv · 2004.03833

Multiplication operators between discrete Hardy spaces on rooted trees

P. Muthukumar·P. Shankar

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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 $\mathbb{T}_{p}$.

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BibTeX RIS

P. Muthukumar, P. Shankar. 2020-04-08. Multiplication operators between discrete Hardy spaces on rooted trees. https://arxiv.org/abs/2004.03833

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