Properties of m-complex symmetric operators

Muneo Cho, Eungil Ko, Ji Eun Lee

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this paper, we study several properties of m-complex symmetric operators. In particular, we prove that if T ε L(H) is an m-complex symmetric operator and N is a nilpotent operator of order n > 2 with TN = NT, then T + N is a (2n+m-2)-complex symmetric operator. Moreover, we investigate the decomposability of T+A and TA where T is an m-complex symmetric operator and A is an algebraic operator. Finally, we provide various spectral relations of such operators. As some applications of these results, we discuss Weyl type theorems for such operators.

Original languageEnglish
Pages (from-to)233-248
Number of pages16
JournalStudia Universitatis Babes-Bolyai Mathematica
Volume62
Issue number2
DOIs
StatePublished - 2017

Keywords

  • Conjugation
  • Decomposable
  • Nilpotent perturbations
  • Weyl type theorems
  • m-complex symmetric operator

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