Invariance of Conjugate Normality Under Similarity
Year: 2024
Author: Cun Wang, Meng Yu, Minyi Liang
Communications in Mathematical Research , Vol. 40 (2024), Iss. 3 : pp. 245–260
Abstract
An operator T on a separable, infinite dimensional, complex Hilbert space H is called conjugate normal if C|T|C=|T∗| for some conjugate linear, isometric involution C on H. This paper focuses on the invariance of conjugate normality under similarity. Given an operator T, we prove that every operator A similar to T is conjugate normal if and only if there exist complex numbers λ1, λ2 such that (T−λ1)(T−λ2)=0.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2024-0002
Communications in Mathematical Research , Vol. 40 (2024), Iss. 3 : pp. 245–260
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: C-normal operators complex symmetric operators similarity.
Author Details
Cun Wang Email
Meng Yu Email
Minyi Liang Email