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Maps preserving some spectral domains of skew products of operators
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2021-09-15 , DOI: 10.1080/03081087.2021.1976716 Y. Bouramdane 1 , M. Ech-Chérif El Kettani 1
中文翻译:
保留算子偏斜积的一些谱域的地图
更新日期:2021-09-15
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2021-09-15 , DOI: 10.1080/03081087.2021.1976716 Y. Bouramdane 1 , M. Ech-Chérif El Kettani 1
Affiliation
Let be an infinite dimensional Hilbert space and be the algebra of all bounded linear operators on . For , let denote the semi-Fredholm domain, the Fredholm domain or the Weyl domain of A in the spectrum, σ(A). We characterize the form of a map ϕ from into itself with range contains the operators of rank at most two and satisfies for all . We also describe those maps on preserving the same spectral set ‘but of Jordan skew-triple product’ ‘of operators’.
中文翻译:
保留算子偏斜积的一些谱域的地图
让是一个无限维的希尔伯特空间,并且是所有有界线性算子的代数. 为了, 让表示谱中A的半 Fredholm 域、Fredholm 域或 Weyl 域, σ ( A )。我们从中表征映射ϕ的形式进入其自身,其范围包含最多两个等级的运算符并满足对全部. 我们还描述了这些地图保留相同的光谱集'但乔丹偏斜三重产品''运营商'。