8 papers
The Sharp Scale Inequality for the Schatten Trace Class
Yong Jiao, Sijie Luo, Lian Wu
In this paper, we establish the metric cotype inequality for the Schatten trace class at the optimal order of the scaling parameter. More precisely, for every integer $…
Talagrand type for noncommutative spaces
Sijie Luo, Yusen Wang, Dejian Zhou
Let be a semi-finite von Neumann algebra. We prove that has Talagrand type , where . As an consequence, th…
The Quantum KKL Inequality
Yong Jiao, Wenlong Lin, Sijie Luo +1
In this paper, we resolve the quantum KKL conjecture of Montanaro and Osborne \cite{MO2010} for quantum Boolean functions on the -qubit hypercube. More precisely, for every self…
Sharp Fractional Riesz Estimates on the Hypercube
Yong Jiao, Sijie Luo, Dmitriy Zanin +1
Let be the -dimensional hypercube equipped with the normalized uniform measure, let be the Walsh gradient and let be the Walsh Laplacian. For eve…
Large Deviation Inequalities for Noncommutative Martingales
Yong Jiao, Sijie Luo, Dejian Zhou
We establish noncommutative analogs of some well-known large deviation inequalities for noncommutative random variables. Firstly, for the noncommutative independent case, we charac…
Almost uniform convergence for noncommutative Vilenkin-Fourier series
Yong Jiao, Sijie Luo, Tiantian Zhao +1
In the present paper, we study almost uniform convergence for noncommutative Vilenkin-Fourier series. Precisely, we establish several noncommutative (asymmetric) maximal inequaliti…
Quantum KKL-type Inequalities Revisited
Yong Jiao, Wenlong Lin, Sijie Luo +1
In the present paper, we develop the random restriction method in the quantum framework. By applying this method, we establish the quantum Eldan-Gross inequality, the quantum Talag…
On noncommutative Hölder inequality of Sukochev and Zanin for weak Schatten class
Yi C. Huang, Sijie Luo
Sukochev and Zanin resolved an open problem due to B. Simon concerning optimal constants in Hölder inequality for the weak Schatten classes of compact operators. In this note we ob…