Open AccessNew estimates for the numerical radius
Author(s) -
Hamid Reza Moradi,
Mohammad Sababheh
Publication year - 2021
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/fil2114957m
Subject(s) - mathematics , hilbert space , multiplicative function , norm (philosophy) , inequality , radius , dissipative system , operator (biology) , pure mathematics , mathematical analysis , computer science , biochemistry , chemistry , physics , computer security , repressor , quantum mechanics , political science , transcription factor , law , gene
In this article, we present new inequalities for the numerical radius of the sum of two Hilbert space operators. These new inequalities will enable us to obtain many generalizations and refinements of some well known inequalities, including multiplicative behavior of the numerical radius and norm bounds. Among many other applications, it is shown that if T is accretive-dissipative, then 1/?2 ||T|| ? ?(T), where ?(?) and ||?||denote the numerical radius and the usual operator norm, respectively. This inequality provides a considerable refinement of the well known inequality 1/2 ||T|| ? ?(T).