Doubly Commuting Semigroups of Isometries
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909767933362176 |
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| author | Namitha, C. H. Sundar, S. Veerabathiran, Shankar |
| author_facet | Namitha, C. H. Sundar, S. Veerabathiran, Shankar |
| contents | In this paper, we discuss the structure of doubly commuting semigroups of isometries. We record a new proof of Cooper's theorem in the Hilbert module setting. We discuss the Fell topology on the set of equivalence classes of irreducible, doubly commuting isometric representations of $\mathbb{R}_{+}^{d}$. We show that if $d$ is finite, the topology is $T_0$. We indicate the pathologies that occur when $d=\infty$. In particular, we show that Wold decomposition fails for isometric representations of $\mathbb{R}_{+}^{\infty}$ and prove that the Fell topology on the set of equivalence classes of irreducible, doubly commuting isometric representations of $\mathbb{R}_{+}^{\infty}$ is not $T_0$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00409 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Doubly Commuting Semigroups of Isometries Namitha, C. H. Sundar, S. Veerabathiran, Shankar Operator Algebras Functional Analysis In this paper, we discuss the structure of doubly commuting semigroups of isometries. We record a new proof of Cooper's theorem in the Hilbert module setting. We discuss the Fell topology on the set of equivalence classes of irreducible, doubly commuting isometric representations of $\mathbb{R}_{+}^{d}$. We show that if $d$ is finite, the topology is $T_0$. We indicate the pathologies that occur when $d=\infty$. In particular, we show that Wold decomposition fails for isometric representations of $\mathbb{R}_{+}^{\infty}$ and prove that the Fell topology on the set of equivalence classes of irreducible, doubly commuting isometric representations of $\mathbb{R}_{+}^{\infty}$ is not $T_0$ |
| title | Doubly Commuting Semigroups of Isometries |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2509.00409 |