On Numerical Radius Inequalities for Operator Matrices. (18th August 2019)

• Record Type: Journal Article
• Authors: Guelfen, Hanane; Kittaneh, Fuad
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 11(2019)
• Page Start: 1231
• Page End: 1241
• Publication Date: 2019-08-18
• Subjects: Inequality -- numerical radius -- operator matrix -- spectral radius; 47A12 -- 47A30 -- 47A63; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1549073
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The aim of this article is to prove several new numerical radius inequalities for n × n operator matrices on a Hilbert space. Let H 1, H 2, …, H n be complex Hilbert spaces, and let T = [ T i j ] be an n × n operator matrix with T i j ∈ B ( H j, H i ) . Among other inequalities, it shown that ω ( T ) ≤ 1 2 ∑ i = 1 n ( w ( T i i ) + ω 2 ( T i i ) + ∑ j = 1 j ≠ i n | | T i j | | 2 ), where ω ( · ) and | | · | | denote the numerical radius and the usual operator norm, respectively.