| 摘要: |
| 本文主要给出了压缩秩1投影对联合数值域的映射Φ的完全刻画.利用投影对的联合数值域自身所具有的性质得到了Φ保持双边保正交性,并且在Hilbert空间维数为$2$时Φ保持秩1投影对的联合数值域,由此我们得到了压缩秩1投影对联合数值域的满射由一个酉算子或反酉算子诱导,从而推广了邓年、钱文华和吴文明在有限维Hilbert空间上保持秩1投影对联合数值域映射的结果. |
| 关键词: 投影对 压缩联合数值域 酉算子 反酉算子 |
| DOI： |
| 分类号:O177.2 |
| 基金项目:重庆市自然科学基金资助(CSTB2025NSCQLZX0057). |
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| MAPPINGS SHRINKING THE JOINT NUMERICAL RANGE OF ANY PAIR OF RANK 1 PROJECTIONS |
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LI Yang, CHEN Shao-bo
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School of Mathematical Science, Chongqing Normal University, Chongqing 401331, China
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| Abstract: |
| This paper characterizes the map Φ which shrinks the joint numerical range of any pair of rank 1 projections. By using the intrinsic properties of the joint numerical range of pairs of projections, this paper demonstrates that Φ preserves orthogonality in both directions and Φ preserves the joint numerical range of any pair of rank 1 projections when the Hilbert space is two-dimensional. It follows that a surjective mapping shrinking the joint numerical range of any pair of rank 1 projections is induced by a unitary or anti-unitary operator, thereby generalizing the results of Deng Nian, Qian Wenhua, and Wu Wenming on mappings that preserve the joint numerical range of any pair of rank 1 projections on flnite-dimensional Hilbert spaces. |
| Key words: pair of projection shrinking joint numerical range unitary anti-unitary |
