On properties of the operator equation TT∗ = T + T∗

Il Ju An, Eungil Ko

Research output: Contribution to journalArticlepeer-review


In this paper, we study properties of the operator equation TT = T+T which T.T. West observed in [12]. We first investigate the structure of solutions T ∈ B(H) of such equation. Moreover, we prove that if T is a polynomial root of solutions of that operator equation, then the spectral mapping theorem holds for Weyl and essential approximate point spectra of T and f (T) satisfies a-Weyl’s theorem for f ∈ H(σ(T)), where H(σ(T)) is the space of functions analytic in an open neighborhood of σ(T).

Original languageEnglish
Pages (from-to)2247-2256
Number of pages10
Issue number6
StatePublished - 2018


  • Operator equations
  • Single valued extension property
  • Spectrum


Dive into the research topics of 'On properties of the operator equation TT∗ = T + T∗'. Together they form a unique fingerprint.

Cite this