Open AccessRemarks on n-normal operators
Author(s) -
Muneo Chō,
Eun Ji Lee,
Kôtarô Tanahashi,
Atsushi Uchiyama
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/fil1815441c
Subject(s) - mathematics , bounded function , hilbert space , domain (mathematical analysis) , operator (biology) , combinatorics , linear operators , pure mathematics , mathematical analysis , biochemistry , chemistry , repressor , transcription factor , gene
Let T be a bounded linear operator on a complex Hilbert space and n,m ? N. Then T is said to be n-normal if T+Tn = TnT+ and (n,m)-normal if T+mTn = TnT+m. In this paper, we study several properties of n-normal, (n,m)-normal operators. In particular, we prove that if T is 2-normal with ?(T) ? (-?(T)) ? {0}, then T is polarloid. Moreover, we study subscalarity of n-normal operators. Also, we prove that if T is (n,m)-normal, then T is decomposable and Weyl?s theorem holds for f (T), where f is an analytic function on ?(T) which is not constant on each of the components of its domain.