Annals of Functional Analysis

Upper bounds for numerical radius inequalities involving off-diagonal operator matrices

Mojtaba Bakherad and Khalid Shebrawi

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In this article, we establish some upper bounds for numerical radius inequalities, including those of 2×2 operator matrices and their off-diagonal parts. Among other inequalities, it is shown that if T=[0XY0], then ωr(T)2r2f2r(|X|)+g2r(|Y|)12f2r(|Y|)+g2r(|X|)12 and ωr(T)2r2f2r(|X|)+f2r(|Y|)12g2r(|Y|)+g2r(|X|)12, where X,Y are bounded linear operators on a Hilbert space H, r1, and f, g are nonnegative continuous functions on [0,) satisfying the relation f(t)g(t)=t (t[0,)). Moreover, we present some inequalities involving the generalized Euclidean operator radius of operators T1,,Tn.

Article information

Ann. Funct. Anal., Volume 9, Number 3 (2018), 297-309.

Received: 6 June 2017
Accepted: 5 September 2017
First available in Project Euclid: 17 October 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A12: Numerical range, numerical radius
Secondary: 47A30: Norms (inequalities, more than one norm, etc.) 47A63: Operator inequalities 47B33: Composition operators

numerical radius off-diagonal part positive operator Young inequality generalized Euclidean operator radius


Bakherad, Mojtaba; Shebrawi, Khalid. Upper bounds for numerical radius inequalities involving off-diagonal operator matrices. Ann. Funct. Anal. 9 (2018), no. 3, 297--309. doi:10.1215/20088752-2017-0029.

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