Almost commuting self-adjoint operators and iterated commutator estimates

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-09-05 DOI:10.1016/j.laa.2025.09.004

Jakob Geisler

引用次数: 0

Abstract

Given two almost commuting self-adjoint operators, a new method for finding exactly commuting operators is presented. For this, a differential equation for self-adjoint Hilbert-Schmidt operators is introduced. Quantitative results are proven that the exactly commuting operators are close to the old ones in the Hilbert-Schmidt norm. The proof relies on a novel estimate in which the norm of the commutator is bounded from above by the norm of the iterated commutators times a constant. This inequality is proven in finite dimensions and lower bounds for the optimal constants are given.

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几乎可交换自伴随算子和迭代换向子估计

给定两个几乎可交换的自伴随算子，给出了一种求精确可交换算子的新方法。为此，引入了自伴随Hilbert-Schmidt算子的微分方程。定量结果证明，在Hilbert-Schmidt范数中，精确交换算子接近旧算子。这个证明依赖于一个新的估计，其中对易子的范数由上面迭代对易子的范数乘以一个常数限定。在有限维上证明了这个不等式，并给出了最优常数的下界。

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

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.