Zobrazeno 1 - 10
of 132
pro vyhledávání: '"Kian, Mohsen"'
Autor:
Kian, Mohsen, Mazraj, Zainab Peymani
We study the Mercer inequality and its operator extension for superquadratic functions. In particular, we give a more general form of the Mercer inequality by replacing some constants by positive operators. As some consequences, our results produce a
Externí odkaz:
http://arxiv.org/abs/2403.17557
Autor:
Kian, Mohsen
Publikováno v:
Linear Algebra and its Applications (2023)
There exist two major subclasses in the class of superquadratic functions, one comprises concave and decreasing functions, while the other consists of convex and monotone increasing functions. Leveraging this distinction, we introduce eigenvalue ineq
Externí odkaz:
http://arxiv.org/abs/2307.04362
Let $A$ and $ B$ be $n\times n$ positive definite complex matrices, let $\sigma$ be a matrix mean, and let $f : [0,\infty)\to [0,\infty)$ be a differentiable convex function with $f(0)=0$. We prove that $$f^{\prime}(0)(A \sigma B)\leq \frac{f(m)}{m}(
Externí odkaz:
http://arxiv.org/abs/2302.08127
Relating to finding possible upper bounds for the probability of error for discriminating between two quantum states, it is well-known that \begin{align*} \mathrm{tr}(A+B) - \mathrm{tr}|A-B|\leq 2\, \mathrm{tr}\big(f(A)g(B)\big) \end{align*} holds fo
Externí odkaz:
http://arxiv.org/abs/2302.07818
Autor:
Kian, Mohsen
Publikováno v:
In Linear Algebra and Its Applications 15 September 2024 697:293-308
Publikováno v:
Anal. Math. Phys. 14 (2024), no. 3, Paper No. 48
Every positive multilinear map between $C^*$-algebras is separately weak$^*$-continuous. We show that the joint weak$^*$-continuity is equivalent to the joint weak$^*$-continuity of the multiplications of $C^*$-algebras under consideration. We study
Externí odkaz:
http://arxiv.org/abs/2202.12798
Autor:
Kian, Mohsen
We investigate how the type of Convexity of the Core function affects the Csisz\'{a}r $f$-divergence functional. A general treatment for the type of convexity has been considered and the associated perspective functions have been studied. In particul
Externí odkaz:
http://arxiv.org/abs/2101.02934
Autor:
Kian, Mohsen, Seo, Yuki
Publikováno v:
Analysis and Mathematical Physics-2021
Employing the notion of operator log-convexity, we study joint concavity$/$ convexity of multivariable operator functions: $(A,B)\mapsto F(A,B)=h\left[ \Phi(f(A))\ \sigma\ \Psi(g(B))\right]$, where $\Phi$ and $\Psi$ are positive linear maps and $\sig
Externí odkaz:
http://arxiv.org/abs/2010.12856
Autor:
Kian, Mohsen, Alomari, Mohammad W.
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}}
Externí odkaz:
http://arxiv.org/abs/2001.10013
Let $\Phi$ be a unital positive linear map and let $A$ be a positive invertible operator. We prove that there exist partial isometries $U$ and $V$ such that \[ |\Phi(f(A))\Phi(A)\Phi(g(A))|\leq U^*\Phi(f(A)Ag(A))U \] and \[\left|\Phi\left(f(A)\right)
Externí odkaz:
http://arxiv.org/abs/2001.09962