Some Generalized Euclidean Operator Radius Inequalities

Alomari, Mohammad W.; Shebrawi, Khalid; Chesneau, Christophe

doi:10.3390/axioms11060285

Cited by 11 publications

(9 citation statements)

References 18 publications

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“…2 + w e (W )ψ |ζ|2 As a consequence of Theorem 3, we can conclude that w e (X ) ≤ ∥X ∥ and w e (W ) ≤ ∥W ∥. Additionally, it is evident that w…”

mentioning

confidence: 66%

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Inequalities for the Euclidean Operator Radius of n-Tuple Operators and Operator Matrices in Hilbert C∗-Modules

Rashid,

Salameh

2024

Symmetry

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This study takes a detailed look at various inequalities related to the Euclidean operator radius. It examines groups of n-tuple operators, studying how they add up and multiply together. It also uncovers a unique power inequality specific to the Euclidean operator radius. The research broadens its scope to analyze how n-tuple operators, when used as parts of 2×2 operator matrices, illustrate inequalities connected to the Euclidean operator radius. By using the Euclidean numerical radius and Euclidean operator norm for n-tuple operators, the study introduces a range of new inequalities. These inequalities not only set limits for the addition, multiplication, and Euclidean numerical radius of n-tuple operators but also help in establishing inequalities for the Euclidean operator radius. This process involves carefully examining the Euclidean numerical radius inequalities of 2×2 operator matrices with n-tuple operators. Additionally, a new inequality is derived, focusing specifically on the Euclidean operator norm of 2×2 operator matrices. Throughout, the research keeps circling back to the idea of finding and understanding symmetries in linear operators and matrices. The paper highlights the significance of symmetry in mathematics and its impact on various mathematical areas.

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“…2 + w e (W )ψ |ζ|2 As a consequence of Theorem 3, we can conclude that w e (X ) ≤ ∥X ∥ and w e (W ) ≤ ∥W ∥. Additionally, it is evident that w…”

mentioning

confidence: 66%

“…If we have a bounded linear operator T on a Hilbert space H, then its norm is defined as ∥T∥ = sup ∥x∥=1 ∥Tx∥, where ∥x∥ denotes the norm of the vector x in the Hilbert space. The Euclidean operator radius extends this concept to a tuple of operators or matrices (see [1][2][3][4]).…”

Section: Introductionmentioning

confidence: 99%

Inequalities for the Euclidean Operator Radius of n-Tuple Operators and Operator Matrices in Hilbert C∗-Modules

Rashid,

Salameh

2024

Symmetry

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“…These concepts are used in different parts of mathematics. Previous research, including the studies referenced in [1][2][3][4][5][6][7][8][9][10], has extensively investigated mathematical inequalities and discovered significant findings. These studies provide a foundation for future research in this field.…”

Section: Introduction and Preliminarymentioning

confidence: 99%

Norm and Numerical Radius Inequalities for Sums of Power Series of Operators in Hilbert Spaces

Altwaijry,

Dragomir,

Feki

2024

Axioms

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The main focus of this paper is on establishing inequalities for the norm and numerical radius of various operators applied to a power series with the complex coefficients h(λ)=∑k=0∞akλk and its modified version ha(λ)=∑k=0∞|ak|λk. The convergence of h(λ) is assumed on the open disk D(0,R), where R is the radius of convergence. Additionally, we explore some operator inequalities related to these concepts. The findings contribute to our understanding of operator behavior in bounded operator spaces and offer insights into norm and numerical radius inequalities.

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“…These inequalities were also reformulated and generalized in [10] but in terms of Cartesian decomposition. Both of them have been generalized recently in [11,12], respectively.…”

Section: Introductionmentioning

confidence: 99%

On the Dragomir Extension of Furuta’s Inequality and Numerical Radius Inequalities

2022

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In this work, some numerical radius inequalities based on the recent Dragomir extension of Furuta’s inequality are obtained. Some particular cases are also provided. Among others, the celebrated Kittaneh inequality reads: wT≤12T+T*. It is proved that wT≤12T+T*−12infx=1Tx,x12−T*x,x122, which improves on the Kittaneh inequality for symmetric and non-symmetric Hilbert space operators. Other related improvements to well-known inequalities in literature are also provided.

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Some Generalized Euclidean Operator Radius Inequalities

Abstract: In this work, some generalized Euclidean operator radius inequalities are established. Refinements of some well-known results are provided. Among others, some bounds in terms of the Cartesian decomposition of a given Hilbert space operator are proven.

Cited by 11 publications

References 18 publications

Inequalities for the Euclidean Operator Radius of n-Tuple Operators and Operator Matrices in Hilbert C∗-Modules

Inequalities for the Euclidean Operator Radius of n-Tuple Operators and Operator Matrices in Hilbert C∗-Modules

Norm and Numerical Radius Inequalities for Sums of Power Series of Operators in Hilbert Spaces

On the Dragomir Extension of Furuta’s Inequality and Numerical Radius Inequalities

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