Inequalities for absolute value operators

Zou, Limin; He, Chu; Qaisar, Shahid

doi:10.1016/j.laa.2012.08.025

Cited by 3 publications

(2 citation statements)

References 10 publications

(14 reference statements)

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“…We write T 1 ≥ T 2 if T 1 and T 2 are self-adjoint operators and if T 1 − T 2 ≥ 0. In [2], we found several inequalities for absolute value operators.…”

Section: Introductionmentioning

confidence: 95%

About the Cauchy–Bunyakovsky–Schwarz Inequality for Hilbert Space Operators

Minculete

2021

Symmetry

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The symmetric shape of some inequalities between two sequences of real numbers generates inequalities of the same shape in operator theory. In this paper, we study a new refinement of the Cauchy–Bunyakovsky–Schwarz inequality for Euclidean spaces and several inequalities for two bounded linear operators on a Hilbert space, where we mention Bohr’s inequality and Bergström’s inequality for operators. We present an inequality of the Cauchy–Bunyakovsky–Schwarz type for bounded linear operators, by the technique of the monotony of a sequence. We also prove a refinement of the Aczél inequality for bounded linear operators on a Hilbert space. Finally, we present several applications of some identities for Hermitian operators.

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“…We write T 1 ≥ T 2 if T 1 and T 2 are self-adjoint operators and if T 1 − T 2 ≥ 0. In [2], we found several inequalities for absolute value operators.…”

Section: Introductionmentioning

confidence: 95%

About the Cauchy–Bunyakovsky–Schwarz Inequality for Hilbert Space Operators

Minculete

2021

Symmetry

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“…Let B(H) be the algebra of all bounded linear operators acting on a complex Hilbert space H. For T ∈ B(H), we denote by |T| the absolute value operator of T, that is, |T| = (T * T) For A, B ∈ B(H), let A = U|A| and B = V|B| be polar decompositions of A and B, respectively. By using a simple method Zou et al [11,Theorem 2.1] obtained an inequality for absolute value operators as follows:…”

Section: Introductionmentioning

confidence: 99%

Operator inequalities related to p-angular distances

Davood

Dehghan

2019

Filomat

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For any nonzero elements x, y in a normed space X, the angular and skew-angular distance is respectively defined by α[x, y] = x x − y y and β[x, y] = x y − y x. Also inequality α ≤ β characterizes inner product spaces. Operator version of α p has been studied by Pečarić, Rajić, and Saito, Tominaga, and Zou et al.In this paper, we study the operator version of p-angular distance β p by using Douglas' lemma. We also prove that the operator version of inequality α p ≤ β p holds for normal and double commute operators. Some examples are presented to show essentiality of these conditions.

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Some Refinements and Generalizations of Bohr’s Inequality

Aljawi,

Conde,

Feki

2024

Axioms

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In this article, we delve into the classic Bohr inequality for complex numbers, a fundamental result in complex analysis with broad mathematical applications. We offer refinements and generalizations of Bohr’s inequality, expanding on the established inequalities of N. G. de Bruijn and Radon, as well as leveraging the class of functions defined by the Daykin–Eliezer–Carlitz inequality. Our novel contribution lies in demonstrating that Bohr’s and Bergström’s inequalities can be derived from one another, revealing a deeper interconnectedness between these results. Furthermore, we present several new generalizations of Bohr’s inequality, along with other notable inequalities from the literature, and discuss their various implications. By providing more comprehensive and verifiable conditions, our work extends previous research and enhances the understanding and applicability of Bohr’s inequality in mathematical studies.

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Inequalities for absolute value operators

Abstract: We present refinements of an inequality which is due to Saito and Tominaga [Linear Algebra Appl. 432 (2010) 3258-3264], and other inequalities for absolute value operators.

Cited by 3 publications

References 10 publications

About the Cauchy–Bunyakovsky–Schwarz Inequality for Hilbert Space Operators

About the Cauchy–Bunyakovsky–Schwarz Inequality for Hilbert Space Operators

Operator inequalities related to p-angular distances

Some Refinements and Generalizations of Bohr’s Inequality

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