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 $\mathcal{H}$ is called conjugate normal if $C|T|C = |T^∗|$ for some conjugate linear, isometric involution $C$ on $\mathcal{H}.$ 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 $λ_1$, $λ_2$ such that $(T−λ_1)(T−λ_2)=0.$
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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.