On preservers of pseudo spectrum of skew Jordan matrix products

IF 0.5 Q3 MATHEMATICS ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2022-10-26 DOI:10.1007/s44146-022-00052-9

M. Bendaoud, A. Benyouness, A. Cade, M. Sarih

引用次数: 0

Abstract

Let $\mathcal {M}_n$ be the space of $n \times n$ complex matrices, and for $\varepsilon > 0$ and $A \in \mathcal {M}_n$, let $\sigma _\varepsilon (A)$ denote the $\varepsilon $-pseudo spectrum of A. Maps $\Phi $ on $\mathcal {M}_n$ which preserve the skew Jordan semi-triple product of matrices in a sense that

$$\sigma _\varepsilon(\Phi(A)\Phi(B)*\Phi(A))= \sigma _\varepsilon (AB*A)\quad \quad (A,B \in \mathcal {M}_n)$$

are characterized, with no surjectivity assumption on them. Analogous description is obtained for the skew Jordan product on matrices, and its variant of infinite dimension is also noted.

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关于偏斜Jordan矩阵乘积伪谱的保持器

让\（\mathcal{M}_n\)是\（n\times n\）复矩阵的空间，对于\（\varepsilon>；0\）和\（A\in\mathcal{M}_n\)，设\（\sigma\varepsilon（A）\）表示A的\（\varepsilon\）-伪谱{M}_n\)在$$\sigma\varepsilon（\Phi（a）\Phi（B）*\Phi（a））=\sigma\\varepsilo（AB*a）\quad\quad（a，B\in\mathcal{M}_n)$$是有特征的，对它们没有满射性假设。得到了矩阵上偏斜Jordan积的相似描述，并注意到它的无穷维变式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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