Some inequalities for adjointable operators on Hilbert $C^*$-modules
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916284562669568 |
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| author | Sababheh, Mohammad Moradi, Hamid Reza Xu, Qingxiang Zhao, Shuo |
| author_facet | Sababheh, Mohammad Moradi, Hamid Reza Xu, Qingxiang Zhao, Shuo |
| contents | The main purpose of this paper is, in the general setting of the adjointable operators on Hilbert $C^*$-modules, to develop two new tools that can be applied to deal with the positive solutions of certain operator equations, the operator norm as well as the numerical radius, respectively. Among other things, the positivity of a $2\times 2$ block operator matrix is clarified without any preconditions on its entries, and a generalized version of the mixed Schwarz inequality with a parameter is derived. Numerical examples are provided to illustrate the non-triviality of this newly obtained inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13479 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some inequalities for adjointable operators on Hilbert $C^*$-modules Sababheh, Mohammad Moradi, Hamid Reza Xu, Qingxiang Zhao, Shuo Functional Analysis The main purpose of this paper is, in the general setting of the adjointable operators on Hilbert $C^*$-modules, to develop two new tools that can be applied to deal with the positive solutions of certain operator equations, the operator norm as well as the numerical radius, respectively. Among other things, the positivity of a $2\times 2$ block operator matrix is clarified without any preconditions on its entries, and a generalized version of the mixed Schwarz inequality with a parameter is derived. Numerical examples are provided to illustrate the non-triviality of this newly obtained inequality. |
| title | Some inequalities for adjointable operators on Hilbert $C^*$-modules |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2402.13479 |