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Wold-type decomposition for left-invertible weighted shifts on a rootless directed tree

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dc.contributor.author Trivedi, Shailesh
dc.date.accessioned 2025-02-13T09:14:31Z
dc.date.available 2025-02-13T09:14:31Z
dc.date.issued 2025-01
dc.identifier.uri https://arxiv.org/abs/2501.01296
dc.identifier.uri http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/17693
dc.description.abstract Let $S_{\lambdab}$ be a bounded left-invertible weighted shift on a rootless directed tree T=(V,E). We address the question of when $S_{\lambdab}$ has Wold-type decomposition. We relate this problem to the convergence of the series $\displaystyle {\tiny \sum_{n = 1}^{\infty} \sum_{u \in G_{v, n}\backslash G_{v, n-1}} \Big(\frac{\lambdab^{(n)}(u)}{\lambdab^{(n)}(v)}\Big)^2},$ v∈V, involving the moments $\lambdab^{(n)}$ of $S^*_{\lambdab}$, where $G_{v, n}=\childn{n}{\parentn{n}{v}}.$ The main result of this paper characterizes all bounded left-invertible weighted shifts $S_{\lambdab}$ on T, which have Wold-type decomposition. en_US
dc.language.iso en en_US
dc.subject Mathematics en_US
dc.subject Functional analysis en_US
dc.title Wold-type decomposition for left-invertible weighted shifts on a rootless directed tree en_US
dc.type Preprint en_US


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