Numerical Radius Inequalities for Commutators of Hilbert Space Operators

Hirzallah, Omar; Kittaneh, Fuad; Shebrawi, Khalid

doi:10.1080/01630563.2011.580875

Cited by 32 publications

(19 citation statements)

References 4 publications

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“…First, we need the following lemma, which has been recently employed in [5]. Part (a) is well-known, and it can be found in [3, p. 10] …”

Section: Numerical Radius Inequalities For the Operator Matrixmentioning

confidence: 99%

“…for all x, y ∈ H. In the inequality (4.11), replacing x and y by Ax and Bx, respectively, we have It should be mentioned here that the inequality (4.10) and its generalization (4.9) have been obtained recently in [5] by a different technique.…”

Section: Ieotmentioning

confidence: 99%

“…Recent numerical radius equalities and inequalities for operator matrices can be found in [1,2], and [5].…”

Section: Introductionmentioning

confidence: 99%

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Numerical Radius Inequalities for Certain 2 × 2 Operator Matrices

Hirzallah

Kittaneh

Shebrawi

2011

Integr. Equ. Oper. Theory

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100

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We prove several numerical radius inequalities for certain 2×2 operator matrices. Among other inequalities, it is shown that if X, Y, Z, and W are bounded linear operators on a Hilbert space, thenAs an application of a special case of the second inequality, it is shown thatwhich is a considerable improvement of the classical inequality X 2 ≤ w(X). Here w(·) and · are the numerical radius and the usual operator norm, respectively.Mathematics Subject Classification (2010). 47A12, 47A30, 47A63, 47B15.

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“…First, we need the following lemma, which has been recently employed in [5]. Part (a) is well-known, and it can be found in [3, p. 10] …”

Section: Numerical Radius Inequalities For the Operator Matrixmentioning

confidence: 99%

Section: Ieotmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Radius Inequalities for Certain 2 × 2 Operator Matrices

Hirzallah

Kittaneh

Shebrawi

2011

Integr. Equ. Oper. Theory

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100

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“…The quantity w(A) is useful in studying perturbation, convergence and approximation problems as well as integrative methods, etc. For more information see [3,6,9,[13][14][15]17]. In [16], it has been shown that if A is an operator in B(H), then…”

Section: Introductionmentioning

confidence: 99%

Generalizations of the Aluthge transform of operators

Shebrawi¹,

Bakherad²

2018

Filomat

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In this paper, first we generalize the definition of Aluthge transform for non-negative continuous functions f, such that f (x) (x) = x (x ≥ 0). Then, by using this definition, we get some numerical radius inequalities. Among other inequalities, it is shown that if A is bounded linear operator on a complex Hilbert space H, then h (w(A)) ≤ 1 4 h 2 (|A|) + h f 2 (|A|) + 1 2 h w Ã f, , where f, are non-negative continuous functions such that f (x) (x) = x (x ≥ 0), h is a non-negative and non-decreasing convex function on [0, ∞) andÃ f, = f (|A|)U (|A|).

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“…Recently, the authors of [10] applied a different approach to obtain a new numerical radius inequality for commutators of Hilbert space operators. They showed that for T 1 ; T 2 ; T 3 ; T 4 2 B.H /;…”

Section: Introductionmentioning

confidence: 99%