论非交换分布式辛钦内型不等式

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-04-29 DOI:10.1112/blms.13055

Yong Jiao, Xingyan Quan, Fedor Sukochev, Dmitriy Zanin

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摘要

本文的目的是为形式为 ∑ k = 1 ∞ x k ⊗ r k $sum _{k=1}^\infty x_k\otimes r_k$ 的数列提供分布估计，其中 { x k } k ⩾ 1 $\lbrace x_k\rbrace _{k\geqslant 1}$ 是非交换洛伦兹空间Λ log 1 / 2 ( M ) $\Lambda _{log ^{1/2}}(\mathcal {M})$ 的元素，而 { r k } k ⩾ 1 $\lbrace r_k\rbrace _{k\geqslant 1}$ 是拉德马赫函数。为此，我们引入了一类新的算子 { P α } α > 0 $\lbrace P_{\alpha }\rbrace _{\alpha >0}$ 与对偶 Cesáro 算子 C * $C^ast$密切相关，并构建了一个具有独立意义的新外推定理。

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On noncommutative distributional Khintchine type inequalities

The purpose of this paper is to provide distributional estimates for the series of the form $\sum_{k = 1}^{\infty} x_{k} \otimes r_{k}$ with ${x_{k}}_{k ⩾ 1}$ being elements from noncommutative Lorentz spaces $Λ_{\log^{1 / 2}} (M)$ and ${r_{k}}_{k ⩾ 1}$ being Rademacher functions. To this end, we introduce a novel class of operators ${P_{α}}_{α > 0}$ that are closely related to the dual Cesáro operator $C^{*}$ and construct a new extrapolation theorem that is of independent interest.