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Hadamards determinant inequality was refined and generalized by Zhang and Yang in [Acta Math. Appl. Sinica 20 (1997) 269-274]. Some special cases of the result were rediscovered recently by Rozanski, Witula and Hetmaniok in [Linear Algebra Appl. 532 (2017) 500-511]. We revisit the result in the case of positive semidefinite matrices, giving a new proof in terms of majorization and a complete description of the conditions for equality in the positive definite case. We also mention a block extension, which makes use of a result of Thompson in the 1960s.
In this article, we explore the celebrated Gr{u}ss inequality, where we present a new approach using the Gr{u}ss inequality to obtain new refinements of operator means inequalities. We also present several operator Gr{u}ss-type inequalities with applications to the numerical radius and entropies.
Consider the trilinear form for twisted convolution on $mathbb{R}^{2d}$: begin{equation*} mathcal{T}_t(mathbf{f}):=iint f_1(x)f_2(y)f_3(x+y)e^{itsigma(x,y)}dxdy,end{equation*} where $sigma$ is a symplectic form and $t$ is a real-valued parameter. I
One may define a trilinear convolution form on the sphere involving two functions on the sphere and a monotonic function on the interval $[-1,1]$. A symmetrization inequality of Baernstein and Taylor states that this form is maximized when the two fu
In this paper, Wielandts inequality for classical channels is extended to quantum channels. That is, an upper bound to the number of times a channel must be applied, so that it maps any density operator to one with full rank, is found. Using this bou
We provide an alternative proof of the classical single-term asymptotics for Toeplitz determinants whose symbols possess Fisher-Hartwig singularities. We also relax the smoothness conditions on the regular part of the symbols and obtain an estimate f