Doubly twisted near-isometries: Classification and a Wold-type decomposition
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913092827348992 |
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| author | Lata, Sneh Negi, Santosh Singh Singh, Dinesh |
| author_facet | Lata, Sneh Negi, Santosh Singh Singh, Dinesh |
| contents | We introduce and study doubly twisted near-isometries. A doubly twisted near-isometry is a tuple of near-isometries satisfying certain relations determined by a prescribed family of unitaries, thereby generalizing the notion of doubly commuting near-isometries. We establish necessary and sufficient conditions for a tuple of near-isometries to admit a Wold-type decomposition and prove that the existence of such a decomposition automatically ensures its uniqueness by providing an explicit description of the summands. Furthermore, we show that every doubly twisted near-isometry admits a Wold-type decomposition. We also characterize unitary equivalence within the class of doubly twisted near-isometries and construct an analytic model for them. Several examples are included to highlight the distinctions between our results and the corresponding results in the setting of doubly twisted isometries. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_02822 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Doubly twisted near-isometries: Classification and a Wold-type decomposition Lata, Sneh Negi, Santosh Singh Singh, Dinesh Functional Analysis 47A13, 47B37, 46E40, 30H10 We introduce and study doubly twisted near-isometries. A doubly twisted near-isometry is a tuple of near-isometries satisfying certain relations determined by a prescribed family of unitaries, thereby generalizing the notion of doubly commuting near-isometries. We establish necessary and sufficient conditions for a tuple of near-isometries to admit a Wold-type decomposition and prove that the existence of such a decomposition automatically ensures its uniqueness by providing an explicit description of the summands. Furthermore, we show that every doubly twisted near-isometry admits a Wold-type decomposition. We also characterize unitary equivalence within the class of doubly twisted near-isometries and construct an analytic model for them. Several examples are included to highlight the distinctions between our results and the corresponding results in the setting of doubly twisted isometries. |
| title | Doubly twisted near-isometries: Classification and a Wold-type decomposition |
| topic | Functional Analysis 47A13, 47B37, 46E40, 30H10 |
| url | https://arxiv.org/abs/2603.02822 |