On the generalized Cauchy dual of closed operators in Hilbert spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929634094874624 |
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| author | Majumdar, Arup Johnson, P. Sam Mohapatra, Ram N. |
| author_facet | Majumdar, Arup Johnson, P. Sam Mohapatra, Ram N. |
| contents | In this paper, we introduce the generalized Cauchy dual $w(T) = T(T^{*}T)^{\dagger}$ of a closed operator $T$ with the closed range between Hilbert spaces and present intriguing findings that characterize the Cauchy dual of $T$. Additionally, we establish the result $w(T^{n}) = (w(T))^{n}$, for all $n \in \mathbb{N}$, where $T$ is a quasinormal EP operator. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_12313 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the generalized Cauchy dual of closed operators in Hilbert spaces Majumdar, Arup Johnson, P. Sam Mohapatra, Ram N. Functional Analysis 47A05, 47B02, 47B20 In this paper, we introduce the generalized Cauchy dual $w(T) = T(T^{*}T)^{\dagger}$ of a closed operator $T$ with the closed range between Hilbert spaces and present intriguing findings that characterize the Cauchy dual of $T$. Additionally, we establish the result $w(T^{n}) = (w(T))^{n}$, for all $n \in \mathbb{N}$, where $T$ is a quasinormal EP operator. |
| title | On the generalized Cauchy dual of closed operators in Hilbert spaces |
| topic | Functional Analysis 47A05, 47B02, 47B20 |
| url | https://arxiv.org/abs/2412.12313 |