The matched projections of idempotents on Hilbert $C^*$-modules
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911104234422272 |
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| author | Tian, Xiaoyi Xu, Qingxiang Fu, Chunhong |
| author_facet | Tian, Xiaoyi Xu, Qingxiang Fu, Chunhong |
| contents | The aim of this paper is to give new characterizations of some fundamental issues about idempotents. In the general setting of adjointable operators on Hilbert $C^*$-modules, a new term of quasi-projection pair is introduced. For each idempotent $Q$, a projection $m(Q)$, called the matched projection of $Q$, is constructed. It is shown that $Q$ and $m(Q)$ as idempotents are homotopic, and $\big(m(Q),Q\big)$ is a quasi-projection pair. Some formulas for $m(Q)$ are derived. Based on these formulas, representations and norm estimations associated with $m(Q)$ are dealt with. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_12984 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The matched projections of idempotents on Hilbert $C^*$-modules Tian, Xiaoyi Xu, Qingxiang Fu, Chunhong Operator Algebras 46L08, 47A05 The aim of this paper is to give new characterizations of some fundamental issues about idempotents. In the general setting of adjointable operators on Hilbert $C^*$-modules, a new term of quasi-projection pair is introduced. For each idempotent $Q$, a projection $m(Q)$, called the matched projection of $Q$, is constructed. It is shown that $Q$ and $m(Q)$ as idempotents are homotopic, and $\big(m(Q),Q\big)$ is a quasi-projection pair. Some formulas for $m(Q)$ are derived. Based on these formulas, representations and norm estimations associated with $m(Q)$ are dealt with. |
| title | The matched projections of idempotents on Hilbert $C^*$-modules |
| topic | Operator Algebras 46L08, 47A05 |
| url | https://arxiv.org/abs/2305.12984 |