| 摘要: |
| 设 $\mathcal{H}$ 为 复Hilbert空间, $\Phi$ 为 $\mathcal{H}$ 中秩 $1$ 投影上的映射,并且压缩秩 $1$ 投影对的联合数值域.我们证明了当 $\mathrm{dim} (\mathcal{H}) > 2$ 且$\Phi$ 为满射时,$\Phi$ 由一个酉算子或反酉算子诱导; 当 $\mathrm{dim} (\mathcal{H})= 2$时, $\Phi$ 为满射, 此时 $\Phi$ 仍由一个酉算子或反酉算子诱导. |
| 关键词: 投影对 压缩联合数值域 酉算子 反酉算子 |
| DOI： |
| 分类号:O23 |
| 基金项目: |
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| Mapping shrinking the joint numerical range of any pair of rank 1 projections |
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Li Yang, Chen Shaobo
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Chongqing Normal University
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| Abstract: |
| Let $\mathcal{H}$ be a complex Hilbert space. Assume that $\Phi$ is a map on the set of rank 1 projections acting on $\mathcal{H}$ and shrinks the joint numerical range of any pair of rank 1 projections. We show that if $\mathrm{dim}(\mathcal{H}) > 2$ and $\Phi$ is surjective, then $\Phi$ is induced by a unitary or an anti-unitary; if $\mathrm{dim}(\mathcal{H}) = 2$, then $\Phi$ is surjective, and we prove that $\Phi$ is still induced by a unitary or an anti-unitary. |
| Key words: Pair of projection Shrinking joint numerical range Unitary Anti-unitary |
