The Forward and Backward Shift on the Hardy Space of a Tree
Functional Analysis
2023-08-23 v1
Abstract
In this paper we initiate the study of the forward and backward shifts on the Hardy space of a tree and the little Hardy space of a tree. In particular, we investigate when these shifts are bounded, find the norm of the shifts if they are bounded, characterize the trees in which they are an isometry, compute the spectrum in some concrete examples, and completely determine when they are hypercyclic.
Keywords
Cite
@article{arxiv.2308.11016,
title = {The Forward and Backward Shift on the Hardy Space of a Tree},
author = {Adán Ángeles-Romero and Rubén A. Martínez Avendaño},
journal= {arXiv preprint arXiv:2308.11016},
year = {2023}
}
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23 pages