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Remarks on the structure of C-normal operators
Linear and Multilinear Algebra ( IF 1.1 ) Pub Date : 2020-05-21 , DOI: 10.1080/03081087.2020.1771254 Cun Wang 1 , Jiayin Zhao 2 , Sen Zhu 1
中文翻译:
C-正规算子结构备注
更新日期:2020-05-21
Linear and Multilinear Algebra ( IF 1.1 ) Pub Date : 2020-05-21 , DOI: 10.1080/03081087.2020.1771254 Cun Wang 1 , Jiayin Zhao 2 , Sen Zhu 1
Affiliation
ABSTRACT
We study a new class of Hilbert space operators, named C-normal operators for C a conjugation on a complex Hilbert space , which were introduced by M. Ptak, K. Simik and A. Wicher. We provide a refined polar decomposition of C-normal operators. It is proved that those invertible ones are norm dense in and each contraction in is a mean of two unitary ones. For a dense class of operators, we prove that their C-normality coincides with C-symmetry. Also some illustrating examples are provided to show that is not closed under several natural operations.
中文翻译:
C-正规算子结构备注
摘要
我们学习一门新课希尔伯特空间算子的集合,命名为C的正态算子C是复希尔伯特空间上的共轭,由 M. Ptak、K. Simik 和 A. Wicher 介绍。我们提供了C正态算子的精化极坐标分解。证明了那些可逆的在每次收缩是两个单一的平均值。对于一类稠密的算子,我们证明了它们的C正态性与C对称性一致。还提供了一些说明性示例以表明在几个自然操作下不关闭。