On [m,C]-symmetric Operators

Muneo Chō; Ji Eun Lee; Jun Tomiyama

doi:10.5666/KMJ.2018.58.4.637

Articles

Kyungpook Mathematical Journal 2018; 58(4): 637-650

Published online December 31, 2018

On [m,C]-symmetric Operators

Muneo Chō, Ji Eun Lee^*, Jun Tomiyama

Department of Mathematics, Kanagawa University, Hiratsuka 259-1293, Japan
e-mail : chiyom01@kanagawa-u.ac.jp

Department of Mathematics and Statistics, Sejong University, Seoul 05006, Korea
e-mail : jieunlee7@sejong.ac.kr and jieun7@ewhain.netjieun7@ewhain.net

Kôtarô Tanahashi
Department of Mathematics, Tohoku Medical and Pharmaceutical University, Sendai 981-8558, Japan
e-mail : tanahasi@tohoku-mpu.ac.jp

Meguro-ku Nakane 11-10-201, Tokyo 152-0031, Japan
e-mail : juntomi@med.email.ne.jp

Received: August 23, 2017; Revised: January 12, 2018; Accepted: October 23, 2018

Abstract

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Abstract

In this paper first we show properties of isosymmetric operators given by M. Stankus [13]. Next we introduce an [m,C]-symmetric operator T on a complex Hilbert space ℋ. We investigate properties of the spectrum of an [m,C]-symmetric operator and prove that if T is an [m,C]-symmetric operator and Q is an n-nilpotent operator, respectively, then T +Q is an [m+2n − 2, C]-symmetric operator. Finally, we show that if T is [m,C]-symmetric and S is [n,D]-symmetric, then T ⊗S is [m+n−1, C ⊗D]-symmetric.

Keywords: Hilbert space, linear operator, conjugation,