Invariance of Conjugate Normality Under Similarity

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 $\mathcal{H}$ 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.

Author Details

Cun Wang

Meng Yu

Minyi Liang