trace inequality
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2021 ◽  
Author(s):  
Pak Tung Ho
Keyword(s):  


2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Giorgi Imerlishvili ◽  
Alexander Meskhi

AbstractWe establish a necessary and sufficient condition on a non-negative locally integrable function v guaranteeing the (trace) inequality\lVert I_{\alpha}f\rVert_{L^{p}_{v}(\mathbb{R}^{n})}\leq C\lVert f\rVert_{L^{p% ,1}(\mathbb{R}^{n})}for the Riesz potential {I_{\alpha}}, where {L^{p,1}(\mathbb{R}^{n})} is the Lorentz space. The same problem is studied for potentials defined on spaces of homogeneous type.



2020 ◽  
Vol 35 (30) ◽  
pp. 2050254
Author(s):  
K. V. Antipin

For bipartite quantum states we obtain lower bounds on two important entanglement measures, concurrence and negativity, studying the inequalities for the expectation value of a projector on some subspace of the Hilbert space. Several applications, including analysis of stability of entanglement under various perturbations of a state, are discussed.





2020 ◽  
Vol 53 (4) ◽  
pp. 402-435
Author(s):  
Jeffrey S. Case & Yi Wang


2020 ◽  
Vol 40 (4) ◽  
pp. 2871-2897 ◽  
Author(s):  
Lina Zhao ◽  
Eun-Jae Park

Abstract In this paper we propose a locally conservative, lowest-order staggered discontinuous Galerkin method for the coupled Stokes–Darcy problem on general quadrilateral and polygonal meshes. This model is composed of Stokes flow in the fluid region and Darcy flow in the porous media region, coupling together through mass conservation, balance of normal forces and the Beavers–Joseph–Saffman condition. Stability of the proposed method is proved. A new regularization operator is constructed to show the discrete trace inequality. Optimal convergence estimates for all the approximations covering low regularity are achieved. Numerical experiments are given to illustrate the performances of the proposed method. The numerical results indicate that the proposed method can be flexibly applied to rough grids such as the trapezoidal grid and $h$-perturbation grid.



Author(s):  
Mohsen Kian ◽  
Mohammad W. Alomari

We show that if $f$ is a non-negative superquadratic function, then $A\mapsto\mathrm{Tr}f(A)$ is a superquadratic function on the matrix algebra. In particular, \begin{align*} \tr f\left( {\frac{{A + B}}{2}} \right) +\tr f\left(\left| {\frac{{A - B}}{2}}\right|\right) \leq \frac{{\tr {f\left( A \right)} + \tr {f\left( B \right)} }}{2} \end{align*} holds for all positive matrices $A,B$. In addition, we present a Klein's inequality for superquadratic functions as $$ \mathrm{Tr}[f(A)-f(B)-(A-B)f'(B)]\geq \mathrm{Tr}[f(|A-B|)] $$ for all positive matrices $A,B$. It gives in particular improvement of Klein's inequality for non-negative convex function. As a consequence, some variants of the Jensen trace inequality for superquadratic functions have been presented.



Author(s):  
Mohammad Alomari

In this work, some operator trace inequalities are proved. An extension of Klein's inequality for all Hermitian matrices is proved. A non-commutative version (or Hansen-Pedersen version) of the Jensen trace inequality is provided as well. A generalization of the result for any positive Hilbert space operators acts on a positive unital linear map is established.



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