ﻻ يوجد ملخص باللغة العربية
In this paper, we prove the convexity of trace functionals $$(A,B,C)mapsto text{Tr}|B^{p}AC^{q}|^{s},$$ for parameters $(p,q,s)$ that are best possible. We also obtain the monotonicity under unital completely positive trace preserving maps of trace functionals of this type. As applications, we extend some results in cite{HP12quasi,CFL16some} and resolve a conjecture in cite{RZ14}. Other conjectures in cite{RZ14} will also be discussed. We also show that some related trace functionals are not concave in general. Such concavity results were expected to hold in cite{Chehade20} to derive equality conditions of data processing inequalities for $alpha-z$ Renyi relative entropies.
A version of Connes trace formula allows to associate a measure on the essential spectrum of a Schrodinger operator with bounded potential. In solid state physics there is another celebrated measure associated with such operators --- the density of s
Consider a function $F(X,Y)$ of pairs of positive matrices with values in the positive matrices such that whenever $X$ and $Y$ commute $F(X,Y)= X^pY^q.$ Our first main result gives conditions on $F$ such that ${rm Tr}[ X log (F(Z,Y))] leq {rm Tr}[X(p
We establish quantitative bounds on the rate of approach to equilibrium for a system with infinitely many degrees of freedom evolving according to a one-dimensional focusing nonlinear Schrodinger equation with diffusive forcing. Equilibrium is descri
In a recent paper we studied an equation (called the simple equation) introduced by one of us in 1963 for an approximate correlation function associated to the ground state of an interacting Bose gas. Solving the equation yields a relation between th
For a given Lipschitz domain $Omega$, it is a classical result that the trace space of $W^{1,p}(Omega)$ is $W^{1-1/p,p}(partialOmega)$, namely any $W^{1,p}(Omega)$ function has a well-defined $W^{1-1/p,p}(partialOmega)$ trace on its codimension-1 bou