### Complex isosymmetric operators

#### 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.

#### Article information

Source
Adv. Oper. Theory (2018), 12 pages.

Dates
Accepted: 17 February 2018
First available in Project Euclid: 3 March 2018

https://projecteuclid.org/euclid.aot/1520046048

Digital Object Identifier
doi:10.15352/aot.1712-1267

Subjects
Primary: 47B25: Symmetric and selfadjoint operators (unbounded)
Secondary: 47B99: None of the above, but in this section

#### Citation

Chō, Muneo; Lee, Ji Eun; Prasad, T.; Tanahashi, Kôtarô. Complex isosymmetric operators. Adv. Oper. Theory, advance publication, 3 March 2018. doi:10.15352/aot.1712-1267. https://projecteuclid.org/euclid.aot/1520046048

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