Related papers: A Lieb-Thirring inequality for singular values

Let $||X||_p=\text{Tr}[(X^\ast X)^{p/2}]^{1/p}$ denote the $p$-Schatten norm of a matrix $X\in M_{n\times n}(\mathbb{C})$, and $\sigma(X)$ the singular values with $\uparrow$ $\downarrow$ indicating its increasing or decreasing…

For positive definite matrices $A$ and $B$, the Araki-Lieb-Thirring inequality amounts to an eigenvalue log-submajorisation relation for fractional powers $$\lambda(A^t B^t) \prec_{w(\log)} \lambda^t(AB), \quad 0<t\le 1,$$ while for…

We provide new estimates on the best constant of the Lieb-Thirring inequality for the sum of the negative eigenvalues of Schr\"odinger operators, which significantly improve the so far existing bounds.

We prove optimal Lieb-Thirring type inequalities for Schr\"odinger and Jacobi operators with complex potentials. Our results bound eigenvalue power sums (Riesz means) by the $L^p$ norm of the potential, where in contrast to the self-adjoint…

Lieb-Thirring type estimates are proved for the sum of powers of negative eigenvalues of a Schr\"odinger type operator $(-\Delta)^l -V\mu$ where $\mu$ is a singular measure in $\mathbb{R}^d,$ satisfying a condition on the measure of balls…

In this paper, we obtain new upper bounds for the Lieb-Thirring inequality on the spheres of any dimension greater than $2$. As far as we have checked, our results improve previous results found in the literature for all dimensions greater…

We show that recent multivariate generalizations of the Araki-Lieb-Thirring inequality and the Golden-Thompson inequality [Sutter, Berta, and Tomamichel, Comm. Math. Phys. (2016)] for Schatten norms hold more generally for all unitarily…

We establish Lieb-Thirring power bounds on discrete eigenvalues of Jacobi operators for Schatten class complex perturbations of periodic and more generally finite gap Jacobi matrices.

The Lieb-Thirring inequalities give a bound on the negative eigenvalues of a Schr\"odinger operator in terms of an $L^p$ norm of the potential. This is dual to a bound on the $H^1$-norms of a system of orthonormal functions. Here we extend…

We derive Lieb-Thirring inequalities for the Riesz means of eigenvalues of order gamma >= 3/4 for fourth order Schr\"odinger operators in arbitrary dimensions. We also consider some extensions to polyharmonic operators, and to systems of…

We examine a number of known inequalities for $L^p$ functions with reverse representations for $s<1$ with complex matrices under the $p$-norms $||X||_p=\text{Tr}[(X^\ast X)^{p/2}]^{1/p}$, and similarly defined quasinorm or antinorm…

For positive semidefinite $n\times n$ matrices $A$ and $B$, the singular value inequality $(2+t)s_{j}(A^{r}B^{2-r}+A^{2-r}B^{r})\leq 2s_{j}(A^{2}+tAB+B^{2})$ is shown to hold for $r=\frac{1}{2}, 1, \frac{3}{2}$ and all $-2<t\leq 2$.

In this paper, we study the $L^{p}$ boundedness and $L^{p}(w)$ boundedness ($1<p<\infty$ and $w$ a Muckenhoupt $A_{p}$ weight) of fractional maximal singular integral operators $T_{\Omega,\alpha}^{\#}$ with homogeneous convolution kernel…

We prove some sufficient conditions implying $l^p$ inequalities of the form $||x||_p \leq ||y||_p$ for vectors $ x, y \in [0,\infty)^n$ and for $p$ in certain positive real intervals. Our sufficient conditions are strictly weaker than the…

The classical Muckenhoupt's $A_p$ condition is necessary and sufficient for the boundedness of the maximal operator $M$ on $L^p(w)$ spaces. In this paper we obtain another characterization of the $A_p$ condition. As a result, we show that…

Extending earlier work of Killip-Simon and Simon-Zlatos, we obtain sum rules for Jacobi matrices in which the a.c. part of the spectral measure and the eigenvalues of the matrix appear on opposite sides of the equation. We use these to…

If T is a fractional vector Riesz transform, 1<p<infinity, and sigma and omega are doubling measures, then the two weight L^{p} norm inequality holds if and only if the quadratic triple testing conditions of Hyt\"onen and Vuorinen hold. We…

Following Eden and Foias we obtain a matrix version of a generalised Sobolev inequality in one-dimension. This allow us to improve on the known estimates of best constants in Lieb-Thirring inequalities for the sum of the negative…

For bounded linear operators $A,B$ on a Hilbert space $\mathcal{H}$ we show the validity of the estimate $$ \sum_{\lambda \in \sigma_d (B)} \dist(\lambda, \overline{\num}(A))^p \leq \| B-A \|_{\mathcal{S}_p}^p$$ and apply it to recover and…

We extend a classical result by Triebel on boundedness of bandlimited multipliers on $L^p(\mathbb{R}^n)$, $0<p\leq 1$, to a vector-valued and matrix-weighted setting with boundedness of the bandlimited multipliers obtained on $L^p(W)$,…