Some New Refinements of Generalized Numerical Radius Inequalities for Hilbert Space Operators

Feki, Kais; Kittaneh, Fuad

doi:10.1007/s00009-021-01927-x

Cited by 10 publications

(4 citation statements)

References 21 publications

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“…(3) The inequalities in (2.23) improve the bounds in (1.2) (see [18]). (4) A generalization of the inequalities in (2.23) are established in [11].…”

Section: Theorem 225 Let T S ∈ Bmentioning

confidence: 84%

“…(1) Notice that the inequalities in (2.23) are already proved by the second author in [18] and by Altwaijry et al in [1]. However, the techniques used here are different from the other proofs.…”

Section: Theorem 225 Let T S ∈ Bmentioning

confidence: 92%

“…Notice that the particular case d = 1 is the A-numerical radius of an operator T which recently attracted the attention of several mathematicians (see, e.g., [2,7,8,15,16,[18][19][20]23] and the references therein). Some interesting properties of A-joint numerical radius of Abounded operators were given in [5,17].…”

Section: Introductionmentioning

confidence: 99%

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Inequalities for the $A$-joint numerical radius of two operators and their applications

Feki

2024

Hacettepe Journal of Mathematics and Statistics

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Let $\big(\mathcal{H}, \langle \cdot, \cdot\rangle \big)$ be a complex Hilbert space and $A$ be a positive (semidefinite) bounded linear operator on $\mathcal{H}$. The semi-inner product induced by $A$ is given by ${\langle x, y\rangle}_A := \langle Ax, y\rangle$, $x, y\in\mathcal{H}$ and defines a seminorm ${\|\cdot\|}_A$ on $\mathcal{H}$. This makes $\mathcal{H}$ into a semi-Hilbert space. The $A$-joint numerical radius of two $A$-bounded operators $T$ and $S$ is given by \begin{align*} \omega_{A,\text{e}}(T,S) = \sup_{\|x\|_A= 1}\sqrt{\big|{\langle Tx, x\rangle}_A\big|^2+\big|{\langle Sx, x\rangle}_A\big|^2}. \end{align*} In this paper, we aim to prove several bounds involving $\omega_{A,\text{e}}(T,S)$. This allows us to establish some inequalities for the $A$-numerical radius of $A$-bounded operators. In particular, we extend the well-known inequalities due to Kittaneh [Studia Math. 168 (2005), no. 1, 73-80]. Moreover, several bounds related to the $A$-Davis-Wielandt radius of semi-Hilbert space operators are also provided.

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“…(3) The inequalities in (2.23) improve the bounds in (1.2) (see [18]). (4) A generalization of the inequalities in (2.23) are established in [11].…”

Section: Theorem 225 Let T S ∈ Bmentioning

confidence: 84%

Section: Theorem 225 Let T S ∈ Bmentioning

confidence: 92%

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Inequalities for the $A$-joint numerical radius of two operators and their applications

Feki

2024

Hacettepe Journal of Mathematics and Statistics

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“…Recently, some generalizations for the concept of numerical radius have been introduced in [2,4,14,16,18]. One of these generalizations is the A-numerical radius of an operator T ∈ B(H ) defined by w A (T ) = sup{| AT x, x | : x ∈ H , Ax, x = 1}, see, e.g., [8,10,17]. Here, A is a positive bounded linear operator on H .…”

Section: Introductionmentioning

confidence: 99%

Numerical radius inequalities of operator matrices from a new norm on B(H)

Bhunia¹,

Bhanja²,

Sain³

et al. 2023

MMN

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This paper is a continuation of a recent work on a new norm, christened the (α, β)norm, on the space of bounded linear operators on a Hilbert space. We obtain some upper bounds for the said norm of n × n operator matrices. As an application of the present study, we estimate bounds for the numerical radius and the usual operator norm of n × n operator matrices, which generalize the existing ones.

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