Open AccessOn properties of the operator equation TT*=T+T*
Author(s) -
Ilsin An,
Eungil Ko
Publication year - 2018
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1806247a
Subject(s) - mathematics , operator (biology) , polynomial , space (punctuation) , pure mathematics , mathematical analysis , biochemistry , chemistry , linguistics , philosophy , repressor , transcription factor , gene
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 2 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(?(T)), where H(?(T)) is the space of functions analytic in an open neighborhood of ?(T).