Multiplication operators on weighted Banach spaces of a tree

TL;DR

This paper investigates multiplication operators on weighted Banach spaces over infinite trees, providing characterizations of boundedness, compactness, spectra, and isometries, and exploring their behavior between different function spaces.

Contribution

It offers new characterizations of multiplication operators on weighted Banach spaces of trees, including spectra and isometries, extending understanding of operator theory in this context.

Findings

Characterized bounded and compact multiplication operators

Determined the spectra of bounded multiplication operators

Established the absence of isometries between certain spaces

Abstract

We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded multiplication operators and characterize the isometries. Finally, we study the multiplication operators between the weighted Banach spaces and the Lipschitz space by characterizing the bounded and the compact operators, determine estimates on the operator norm, and show there are no isometries.