The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Sever S Dragomir - One of the best experts on this subject based on the ideXlab platform.
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Some Reverses of the Cauchy-Schwarz Inequality for Complex Functions of Self-adjoint Operators in Hilbert spaces
Mathematical Inequalities & Applications, 2014Co-Authors: Sever S Dragomir, Mohammad Sal Moslehian, Yeol Je ChoAbstract:We give some ratio and difference reverses of the Cauchy–Schwarz Inequality for complex functions of self-adjoint operators in Hilbert spaces, under suitable assumptions for the involved operators. Several examples for particular functions of interest are provided as well. Mathematics subject classification (2010): 47A63, 47A99.
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power series inequalities via a refinement of the Schwarz Inequality
Integral Transforms and Special Functions, 2012Co-Authors: Alawiah Ibrahim, Sever S DragomirAbstract:In this paper, we obtain some inequalities for functions defined by a power series with nonnegative coefficients. In order to obtain these inequalities, a refinement of the Schwarz Inequality in inner product spaces is utilized. Natural applications for some elementary functions of interest are also provided.
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refinements of the cauchy bunyakovsky Schwarz Inequality for functions of selfadjoint operators in hilbert spaces
Linear & Multilinear Algebra, 2011Co-Authors: Sever S DragomirAbstract:Some inequalities for continuous functions of selfadjoint operators in Hilbert spaces that improve the Cauchy–Bunyakovsky–Schwarz Inequality, are given.
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Schwarz and gruss type inequalities for c seminorms and positive linear functionals on banach modules
Linear Algebra and its Applications, 2011Co-Authors: A G Ghazanfari, Sever S DragomirAbstract:Abstract Let A be a unital Banach ∗-algebra, γ a C ∗ -seminorm or a positive linear functional on A and X be a semi-inner product A -module. We define a real function Γ on X by Γ ( x ) = ( γ ( x , x > ) ) 1 / 2 and show that the Schwarz Inequality holds, therefore ( X , Γ ) is a semi-Hilbert A -module. We also obtain some Gruss type inequalities for C ∗ -seminorms and positive linear functionals on A .
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some inequalities for power series of selfadjoint operators in hilbert spaces via reverses of the Schwarz Inequality
Integral Transforms and Special Functions, 2009Co-Authors: Sever S DragomirAbstract:In this paper, we obtain some operator inequalities for functions defined by power series with real coefficients and, more specifically, with nonnegative coefficients. In order to obtain these inequalities, some recent reverses of the Schwarz Inequality for vectors in inner product spaces are utilized. Natural applications for some elementary functions of interest are also provided.
Jan Chwedeńczuk - One of the best experts on this subject based on the ideXlab platform.
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cauchy Schwarz Inequality for general measurements as an entanglement criterion
Quantum Information Processing, 2016Co-Authors: Tomasz Wasak, Piotr Szańkowski, Marek Trippenbach, Jan ChwedeńczukAbstract:Considering the broadest set of measurements allowed by quantum mechanics, we demonstrate that the violation Cauchy---Schwarz Inequality for any-order correlation function signals the entanglement among bosons. Our result is general--it applies to any system of bosons, even when the number of particles is not fixed, provided that there is no coherence between different number states.
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Cauchy-Schwarz Inequality and particle entanglement
Physical Review A, 2014Co-Authors: Tomasz Wasak, Piotr Szańkowski, Paweł Ziń, Marek Trippenbach, Jan ChwedeńczukAbstract:Recently, violation of the Cauchy-Schwarz Inequality by the second-order correlation function was reported in a collection of ultracold bosons [Kheruntsyan et al., Phys. Rev. Lett. 108, 260401 (2012)]. We show that the observation of this effect proves the presence of particle entanglement in a many-body system of bosons. Our derivation is based on the analogy between the coherent states of electromagnetic fields and separable states of massive particles. The presented argument applies to any quantum system of identical bosons with either a fixed or a fluctuating number of particles, provided that there is no coherence between different number states.
Tomasz Wasak - One of the best experts on this subject based on the ideXlab platform.
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cauchy Schwarz Inequality for general measurements as an entanglement criterion
Quantum Information Processing, 2016Co-Authors: Tomasz Wasak, Piotr Szańkowski, Marek Trippenbach, Jan ChwedeńczukAbstract:Considering the broadest set of measurements allowed by quantum mechanics, we demonstrate that the violation Cauchy---Schwarz Inequality for any-order correlation function signals the entanglement among bosons. Our result is general--it applies to any system of bosons, even when the number of particles is not fixed, provided that there is no coherence between different number states.
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Cauchy-Schwarz Inequality and particle entanglement
Physical Review A, 2014Co-Authors: Tomasz Wasak, Piotr Szańkowski, Paweł Ziń, Marek Trippenbach, Jan ChwedeńczukAbstract:Recently, violation of the Cauchy-Schwarz Inequality by the second-order correlation function was reported in a collection of ultracold bosons [Kheruntsyan et al., Phys. Rev. Lett. 108, 260401 (2012)]. We show that the observation of this effect proves the presence of particle entanglement in a many-body system of bosons. Our derivation is based on the analogy between the coherent states of electromagnetic fields and separable states of massive particles. The presented argument applies to any quantum system of identical bosons with either a fixed or a fluctuating number of particles, provided that there is no coherence between different number states.
Paul D. Lett - One of the best experts on this subject based on the ideXlab platform.
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Violation of the Cauchy-Schwarz Inequality in the macroscopic regime.
Physical review letters, 2008Co-Authors: Alberto M. Marino, Vincent Boyer, Paul D. LettAbstract:We have observed a violation of the Cauchy-Schwarz Inequality in the macroscopic regime by more than 8 standard deviations. The violation has been obtained while filtering out only the low-frequency noise of the quantum-correlated beams that results from the technical noise of the laser used to generate them. We use bright intensity-difference squeezed beams produced by four-wave mixing as the source of the correlated fields. We also demonstrate that squeezing does not necessarily imply a violation of the Cauchy-Schwarz Inequality.
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Violation of Cauchy-Schwarz Inequality in Continuous-Variable Regime
Frontiers in Optics 2007 Laser Science XXIII Organic Materials and Devices for Displays and Energy Conversion, 2007Co-Authors: Alberto M. Marino, Vincent Boyer, Paul D. LettAbstract:We have observed a violation of the Cauchy-Schwarz Inequality in the continuous-variable regime with the use of bright relative-intensity squeezed beams. The relation between the squeezing spectrum and the g(2)functions is studied.
Silvestru Sever Dragomir - One of the best experts on this subject based on the ideXlab platform.
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operator refinements of Schwarz Inequality in inner product spaces
Linear & Multilinear Algebra, 2019Co-Authors: Silvestru Sever DragomirAbstract:Some improvements of the celebrated Schwarz Inequality in complex inner product spaces in terms of selfadjoint operators 0≤A≤1H are given. Applications for orthonormal families of vectors are also ...
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improving Schwarz Inequality in inner product spaces
Linear & Multilinear Algebra, 2019Co-Authors: Silvestru Sever DragomirAbstract:AbstractSome improvements of the celebrated Schwarz Inequality in complex inner product spaces are given. Applications for n-tuples of complex numbers are provided.
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reverses of Schwarz Inequality in inner product spaces with applications
Mathematische Nachrichten, 2015Co-Authors: Silvestru Sever DragomirAbstract:New reverses of the Schwarz Inequality in complex inner products spaces with applications for bounded linear operators are given. Some Gruss' type inequalities and their applications for numerical radius and the operator norm are provided as well.
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a survey on cauchy bunyakovsky Schwarz Inequality for power series
2014Co-Authors: Alawiah Ibrahim, Silvestru Sever DragomirAbstract:In this paper, we present a survey of some recent results for the celebrated Cauchy–Bunyakovsky–Schwarz Inequality for functions defined by power series with nonnegative coefficients. Particular examples for fundamental functions of interest are presented. Applications for some special functions are given as well.
