## Abstract

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 language | English |
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Pages (from-to) | 2247-2256 |

Number of pages | 10 |

Journal | Filomat |

Volume | 32 |

Issue number | 6 |

DOIs | |

State | Published - 2018 |

## Keywords

- Operator equations
- Single valued extension property
- Spectrum