Characterizations of the semi-harmonious and harmonious quasi-projection pairs on Hilbert $C^*$-modules
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908492473827328 |
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| author | Tian, Xiaoyi Xu, Qingxiang Fu, Chunhong |
| author_facet | Tian, Xiaoyi Xu, Qingxiang Fu, Chunhong |
| contents | For each adjointable idempotent $Q$ on a Hilbert $C^*$-module $H$, a specific projection $m(Q)$ called the matched projection of $Q$ was introduced recently due to the characterization of the minimum value among all the distances from projections to $Q$. Inspired by the relationship between $m(Q)$ and $Q$, another term called the quasi-projection pair $(P,Q)$ was also introduced recently, where $P$ is a projection on $H$ satisfying $Q^*=(2P-I)Q(2P-I)$, in which $Q^*$ is the adjoint operator of the idempotent $Q$ and $I$ is the identity operator on $H$. This paper aims to make systematical characterizations of the semi-harmonious and harmonious quasi-projection pairs on Hilbert $C^*$-modules, and meanwhile to provide examples illustrating the non-triviality of the associated characterizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20062 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterizations of the semi-harmonious and harmonious quasi-projection pairs on Hilbert $C^*$-modules Tian, Xiaoyi Xu, Qingxiang Fu, Chunhong Operator Algebras Functional Analysis For each adjointable idempotent $Q$ on a Hilbert $C^*$-module $H$, a specific projection $m(Q)$ called the matched projection of $Q$ was introduced recently due to the characterization of the minimum value among all the distances from projections to $Q$. Inspired by the relationship between $m(Q)$ and $Q$, another term called the quasi-projection pair $(P,Q)$ was also introduced recently, where $P$ is a projection on $H$ satisfying $Q^*=(2P-I)Q(2P-I)$, in which $Q^*$ is the adjoint operator of the idempotent $Q$ and $I$ is the identity operator on $H$. This paper aims to make systematical characterizations of the semi-harmonious and harmonious quasi-projection pairs on Hilbert $C^*$-modules, and meanwhile to provide examples illustrating the non-triviality of the associated characterizations. |
| title | Characterizations of the semi-harmonious and harmonious quasi-projection pairs on Hilbert $C^*$-modules |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2502.20062 |