Advances in Operator Theory

Complex isosymmetric operators

Muneo Chō, Ji Eun Lee, T. Prasad, and Kôtarô Tanahashi

Advance publication

This article is in its final form and can be cited using the date of online publication and the DOI.

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

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

Permanent link to this document

Digital Object Identifier

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

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


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.

Export citation


  • M. Chō, E. Ko, and J. E. Lee, On $(m, C)$-isometric operators, Complex Anal. Oper. Theory 10 (2016), no. 8, 1679–1694.
  • M. Chō, E. Ko, and J. E. Lee, On $m$-complex symmetric operators II, Mediterr. J. Math. 13 (2016), no. 5, 3255–3264.
  • M. Chō, J. E. Lee, K. Tanahashi, and J. Tomiyama, On $[m,C]$-symmetric operators, Kyungpook Math. J. (to appear).
  • P. R. Halmos, A Hilbert space problem book, Second edition, Springer-Verlag, New York, 1982.
  • S. R. Garcia and M. Putinar, Complex symmetric operators and applications, Trans. Amer. Math. Soc. 358 (2006), no. 3, 1285–1315.
  • S. R. Garcia and M. Putinar, Complex symmetric operators and applications II, Trans. Amer. Math. Soc. 359 (2007), no. 8, 3913–3931.
  • S. R. Garcia and W. R. Wogen, Some new classes of complex symmetric operators, Trans. Amer. Math. Soc. 362 (2010), no. 11, 6065–6077.
  • M. Stankus, $m$-isometries, $n$-symmetries and other linear transformations which are hereditary roots, Integral Equations Operator Theory 75 (2013), 301–321.