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 |
|---|---|
| Pages (from-to) | 2247-2256 |
| Number of pages | 10 |
| Journal | Filomat |
| Volume | 32 |
| Issue number | 6 |
| DOIs | |
| State | Published - 2018 |
Bibliographical note
Funding Information:This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827). The second author was supported by Basic Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2016R1D1A1B03931937).
Publisher Copyright:
© 2018, University of Nis. All rights reserved.
Keywords
- Operator equations
- Single valued extension property
- Spectrum