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Summer 2018 Complex isosymmetric operators
Muneo Chō, Ji Eun Lee, T. Prasad, Kôtarô Tanahashi
Adv. Oper. Theory 3(3): 620-631 (Summer 2018). DOI: 10.15352/aot.1712-1267

Abstract

In this paper, we introduce complex isosymmetric and $(m,n,C)$-isosymmetric operators on a Hilbert space $\mathcal H$ and study properties of such operators. In particular, we prove that if $T \in {\mathcal B}(\mathcal H)$ is an $(m,n,C)$-isosymmetric operator and $N$ is a $k$-nilpotent operator such that $T$ and $N$ are $C$-doubly commuting, then $T + N$ is an $(m+2k-2, n+2k-1,C)$-isosymmetric operator. Moreover, we show that if $T$ is $(m,n,C)$-isosymmetric and if $S$ is $(m',D)$-isometric and $n'$-complex symmetric with a conjugation $D$, then $T \otimes S$ is $(m+m'-1,n+n'-1,C \otimes D)$-isosymmetric.

Citation

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Muneo Chō. Ji Eun Lee. T. Prasad. Kôtarô Tanahashi. "Complex isosymmetric operators." Adv. Oper. Theory 3 (3) 620 - 631, Summer 2018. https://doi.org/10.15352/aot.1712-1267

Information

Received: 3 December 2017; Accepted: 17 February 2018; Published: Summer 2018
First available in Project Euclid: 3 March 2018

zbMATH: 06902455
MathSciNet: MR3795103
Digital Object Identifier: 10.15352/aot.1712-1267

Subjects:
Primary: 47B25
Secondary: 47B99

Keywords: $(m,C)$-isometric operator , complex isosymmetric operator , complex symmetric operator , isosymmetric operator

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.3 • No. 3 • Summer 2018
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