Wold-type decomposition for left-invertible weighted shifts on a rootless directed tree
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910770445418496 |
|---|---|
| author | Chavan, Sameer Trivedi, Shailesh |
| author_facet | Chavan, Sameer Trivedi, Shailesh |
| contents | Let $S_{\lambdab}$ be a bounded left-invertible weighted shift on a rootless directed tree $\mathcal T=(V, \mathcal E).$ We address the question of when $S_{\lambdab}$ has Wold-type decomposition. We relate this problem to the convergence of the series $\displaystyle {\tiny \sum_{n = 1}^{\infty} \sum_{u \in G_{v, n}\backslash G_{v, n-1}} \Big(\frac{\lambdab^{(n)}(u)}{\lambdab^{(n)}(v)}\Big)^2},$ $v \in V,$ 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 $\mathcal T,$ which have Wold-type decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wold-type decomposition for left-invertible weighted shifts on a rootless directed tree Chavan, Sameer Trivedi, Shailesh Functional Analysis Primary 47B37, Secondary 05C20 Let $S_{\lambdab}$ be a bounded left-invertible weighted shift on a rootless directed tree $\mathcal T=(V, \mathcal E).$ We address the question of when $S_{\lambdab}$ has Wold-type decomposition. We relate this problem to the convergence of the series $\displaystyle {\tiny \sum_{n = 1}^{\infty} \sum_{u \in G_{v, n}\backslash G_{v, n-1}} \Big(\frac{\lambdab^{(n)}(u)}{\lambdab^{(n)}(v)}\Big)^2},$ $v \in V,$ 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 $\mathcal T,$ which have Wold-type decomposition. |
| title | Wold-type decomposition for left-invertible weighted shifts on a rootless directed tree |
| topic | Functional Analysis Primary 47B37, Secondary 05C20 |
| url | https://arxiv.org/abs/2501.01296 |