Cauchy dual and Wold-type decomposition for bi-regular covariant representations
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913211859599360 |
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| author | Saini, Dimple |
| author_facet | Saini, Dimple |
| contents | The notion of Cauchy dual for left-invertible covariant representations was studied by Trivedi and Veerabathiran. Using the Moore-Penrose inverse, we extend this notion for the covariant representations having closed range and explore several useful properties. We obtain a Wold-type decomposition for {regular} completely bounded covariant representation whose Moore-Penrose inverse is regular. Also, we discuss an example related to the non-commutative bilateral weighted shift. We prove that the Cauchy dual of the concave covariant representation $(σ, V)$ modulo $N(\wV)$ is hyponormal modulo $N(\wV)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_09345 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cauchy dual and Wold-type decomposition for bi-regular covariant representations Saini, Dimple Functional Analysis 46L08 47A15 (Primary ) 47B38, 47L30, 47L55 (Secondary) The notion of Cauchy dual for left-invertible covariant representations was studied by Trivedi and Veerabathiran. Using the Moore-Penrose inverse, we extend this notion for the covariant representations having closed range and explore several useful properties. We obtain a Wold-type decomposition for {regular} completely bounded covariant representation whose Moore-Penrose inverse is regular. Also, we discuss an example related to the non-commutative bilateral weighted shift. We prove that the Cauchy dual of the concave covariant representation $(σ, V)$ modulo $N(\wV)$ is hyponormal modulo $N(\wV)$. |
| title | Cauchy dual and Wold-type decomposition for bi-regular covariant representations |
| topic | Functional Analysis 46L08 47A15 (Primary ) 47B38, 47L30, 47L55 (Secondary) |
| url | https://arxiv.org/abs/2305.09345 |