Numerical radius inequalities for certain 2 × 2 operator matrices II

Shebrawi, Khalid

doi:10.1016/j.laa.2017.02.019

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Clearly • • a Induces A Seminorm On1

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Cited by 40 publications

(23 citation statements)

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“…This paper is devoted also to prove several new A-numerical radius inequalities of certain 2 × 2 operator matrices. Some of the obtained results cover and extend the following works [9,19,21].…”

Section: Clearly • • a Induces A Seminorm Onsupporting

confidence: 84%

Some bounds for the $\mathbb{A}$-numerical radius of certain $2 \times 2$ operator matrices

Feki

2021

Hacettepe Journal of Mathematics and Statistics

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Section: Clearly • • a Induces A Seminorm Onsupporting

confidence: 84%

Some bounds for the $\mathbb{A}$-numerical radius of certain $2 \times 2$ operator matrices

Feki

2021

Hacettepe Journal of Mathematics and Statistics

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“…Motivated by theoretical study and applications, there have been many generalizations of the numerical radius (e.g., see [3,6,9,15,17,19,20,26,27,28,29,34]). One of these generalizations is the A-numerical radius of an operator T ∈ B(H) defined by…”

Section: Introductionmentioning

confidence: 99%

A-numerical radius inequalities for semi-Hilbertian space operators

Zamani

2019

Linear Algebra and its Applications

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Let A be a positive bounded operator on a Hilbert space H, ·, · . The semi-inner product x, y A := Ax, y , x, y ∈ H induces a semi-norm · A on H. Let T A and w A (T ) denote the A-operator semi-norm and the A-numerical radius of an operator T in semi-Hilbertian space H, · A , respectively. In this paper, we prove the following characterization of w A (T ) 2010 Mathematics Subject Classification. Primary 47A05; Secondary 46C05, 47B65, 47A12.

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“…We develop upper bounds for the norm of the product of two positive operators and that of the sum of two operators. Also we show with numerical examples that these bounds improve on the bound obtained by Shebrawi [18]. Finally, as an application of these numerical radius inequalities of 2 × 2 operator matrices, we estimate bounds for the zeros of a monic polynomial.…”

Section: Introductionmentioning

confidence: 57%

“…is equivalent to the operator norm. Various numerical radius inequalities improving (1.1) have been studied in [5,10,12,[16][17][18][19]. Kittaneh [13] improved on the inequality (1.1) to prove that…”

Section: Introductionmentioning

confidence: 99%