Norm attainment of a class of block operator matrices
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866916044479660032 |
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| author | Wu, Kangjian Ling, Jiayu Xu, Qingxiang |
| author_facet | Wu, Kangjian Ling, Jiayu Xu, Qingxiang |
| contents | Given complex numbers $a, b, c$ and a non-negative continuous function $φ$ defined on $[0, +\infty)$, consider the $2 \times 2$ matrix $$ M_t = \begin{pmatrix} a & t \\ ct & bφ(t) \end{pmatrix}, \quad t \in [0, +\infty). $$ We establish conditions for the strict monotonicity of the norm function $t \mapsto \|M_t\|$. As an application, we characterize the norm attainment of the corresponding block operator matrix $$ T = \begin{pmatrix} aI_H & A \\ cA^* & bφ(|A|) \end{pmatrix},$$ where $I_H$ is the identity operator on a Hilbert space $H$ and $A$ is a bounded linear operator from another Hilbert space to $H$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25283 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Norm attainment of a class of block operator matrices Wu, Kangjian Ling, Jiayu Xu, Qingxiang Functional Analysis Given complex numbers $a, b, c$ and a non-negative continuous function $φ$ defined on $[0, +\infty)$, consider the $2 \times 2$ matrix $$ M_t = \begin{pmatrix} a & t \\ ct & bφ(t) \end{pmatrix}, \quad t \in [0, +\infty). $$ We establish conditions for the strict monotonicity of the norm function $t \mapsto \|M_t\|$. As an application, we characterize the norm attainment of the corresponding block operator matrix $$ T = \begin{pmatrix} aI_H & A \\ cA^* & bφ(|A|) \end{pmatrix},$$ where $I_H$ is the identity operator on a Hilbert space $H$ and $A$ is a bounded linear operator from another Hilbert space to $H$. |
| title | Norm attainment of a class of block operator matrices |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2605.25283 |