Open AccessImproved inequalities for the extension of Euclidean numerical radius
Author(s) -
Akram Bajmaeh Babri,
Mohsen Omidvar Erfanian
Publication year - 2019
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/fil1914519b
Subject(s) - mathematics , extension (predicate logic) , radius , euclidean geometry , inequality , combinatorics , euclidean distance , mathematical analysis , pure mathematics , geometry , computer security , computer science , programming language
This paper aims to discuss inequalities involving extension of Euclidean numerical radius. We obtain a refinement of the inequality shown by Sattari et al. We give an improvement of the inequality presented by Kittaneh for the numerical radius. In fact we show that if T ? B(H), then ?2(T) ? 1/2 ||T*T + TT*||-inf ||x||=1 ?(x), where ?(x) = ?(|T|- ?|T|x,x?|2 + ||T*|- ?|T*|x,x?|2)x,x?.