Functional L1-Lp inequalities in the CAR algebra

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2024-10-15 DOI:10.1016/j.jfa.2024.110700

Yong Jiao, Sijie Luo, Dejian Zhou

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引用次数: 0

Abstract

In the present paper, we use the semigroup method to investigate various functional inequalities invoking

L_{1}

and

L_{p}

norms in the framework of canonical anti-commuting relations algebra (CAR algebra for short). As the main results, we obtain the Poincaré inequality for Talagrand type sum, Eldan-Gross inequality for projections, and the Talagrand influence inequality along with its strengthening form in the CAR algebra. All our results strengthen the noncommutative Poincaré inequality of Efraim and Lust-Piquard at several points. We conclude the paper with two applications of our inequalities. In the first application, we apply the noncommutative Eldan-Gross inequality to derive two KKL-type inequalities in the CAR algebra, which are closely related to the quantum KKL conjecture of Montanaro and Osborne. The second application is the CAR algebra counterpart of the superconcentration phenomenon derived from the noncommutative Talagrand influence inequality.

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CAR 代数中的函数 L1-Lp 不等式

在本文中，我们使用半群方法研究了在典型反交换关系代数（简称 CAR 代数）框架内援引 L1 和 Lp 准则的各种函数不等式。作为主要结果，我们得到了塔拉格兰德型和的庞加莱不等式、投影的埃尔丹-格罗斯不等式和塔拉格兰德影响不等式及其在 CAR 代数中的加强形式。我们的所有结果都在若干点上加强了埃弗拉伊姆和卢斯特-皮夸德的非交换泊恩卡雷不等式。最后，我们以两个不等式的应用来结束本文。在第一个应用中，我们应用非交换埃尔丹-格罗斯不等式推导出 CAR 代数中的两个 KKL 型不等式，它们与蒙塔纳罗和奥斯本的量子 KKL 猜想密切相关。第二个应用是非交换塔拉格朗影响不等式推导出的 CAR 代数对应的超集中现象。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis