Some strong limit theorems for weighted sums of measurable operators

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2021-12-24 DOI:10.1142/s0219025721500223

N. V. Huan, N. Quang

引用次数: 0

Abstract

The aim of this study is to provide some strong limit theorems for weighted sums of measurable operators. The almost uniform convergence and the bilateral almost uniform convergence are considered. As a result, we derive the strong law of large numbers for sequences of successively independent identically distributed measurable operators without using the noncommutative version of Kolmogorov’s inequality.

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可测算子加权和的一些强极限定理

本文的目的是为可测算子的加权和提供一些强极限定理。考虑了近似一致收敛和双侧近似一致收敛。在不使用Kolmogorov不等式的非交换版本的情况下，我们得到了连续独立同分布可测算子序列的强大数定律。

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

Infinite Dimensional Analysis Quantum Probability and Related Topics 数学-统计学与概率论

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： In the past few years the fields of infinite dimensional analysis and quantum probability have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. The number of first-class papers in these fields has grown at the same rate. This is currently the only journal which is devoted to these fields. It constitutes an essential and central point of reference for the large number of mathematicians, mathematical physicists and other scientists who have been drawn into these areas. Both fields have strong interdisciplinary nature, with deep connection to, for example, classical probability, stochastic analysis, mathematical physics, operator algebras, irreversibility, ergodic theory and dynamical systems, quantum groups, classical and quantum stochastic geometry, quantum chaos, Dirichlet forms, harmonic analysis, quantum measurement, quantum computer, etc. The journal reflects this interdisciplinarity and welcomes high quality papers in all such related fields, particularly those which reveal connections with the main fields of this journal.