Continuity of multiplication in projective limit algebras and applications to amenability

IF 1.2 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2025-05-15 DOI:10.1007/s43034-025-00431-7

Krzysztof Piszczek

引用次数: 0

Abstract

We study Köthe PDF-algebras. Using two (different yet natural) definitions of multiplication we obtain a wide class of natural algebras with either discontinuous or continuous multiplication. In this last case, we are able to fully characterize amenable Köthe PDF-algebras in terms of the defining Köthe matrix. This characterization shows an interesting and unexpected relation between algebraic and topological structures of amenable Köthe PDF-algebras.

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射影极限代数中乘法的连续性及其在适应性上的应用

我们学习Köthe pdf代数。利用乘法的两种（不同但自然的）定义，我们得到了一类广泛的具有不连续或连续乘法的自然代数。在最后一种情况下，我们能够根据定义的Köthe矩阵完全表征可服从的Köthe pdf -代数。这种表征显示了可调谐Köthe pdf代数的代数和拓扑结构之间有趣和意想不到的关系。

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

Annals of Functional Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory. Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.