为每个无限广度半网格构建非AMNM加权卷积代数

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2024-11-06 DOI:10.1016/j.jfa.2024.110735

Yemon Choi , Mahya Ghandehari , Hung Le Pham

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引用次数: 0

摘要

巴拿赫交换代数的 AMNM 特性是乘法线性函数的乌兰稳定性的一种形式。我们的研究表明，在任何无限宽的半网格上，我们都可以构造一个权值，由此得到的加权卷积代数不具有 AMNM 性质。我们的研究是始于 [4] 并延续于 [5] 的三部曲的顶点。特别是，我们通过建立具有拉姆齐理论色彩的联合封闭集系统二分法，得到了 [5] 主要结果的完善。

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Constructing non-AMNM weighted convolution algebras for every semilattice of infinite breadth

The AMNM property for commutative Banach algebras is a form of Ulam stability for multiplicative linear functionals. We show that on any semilattice of infinite breadth, one may construct a weight for which the resulting weighted convolution algebra fails to have the AMNM property. Our work is the culmination of a trilogy started in [4] and continued in [5]. In particular, we obtain a refinement of the main result of [5], by establishing a dichotomy for union-closed set systems that has a Ramsey-theoretic flavour.

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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