论文标题
半合格组的拓扑修正性
Topological Amenability of Semihypergroups
论文作者
论文摘要
在本文中，我们介绍并探讨了（局部紧凑的）半播种组的拓扑理由的概念。在某些概率度量的收敛性，卷积的总变化和某些函数的转换以及相关量度衡量标准的F-代数性质方面，我们获得了相同的几种固定，ergodic和Banach代数表征。我们进一步研究了卷积产品的限制与量子量限制对亚近气组的限制之间的相互作用。最后，我们讨论并表征了子隔膜组的拓扑休斯，从父级半乳皮组的相应测度代数上获得的某些不变特性。反过来，这为J. Wong在1980年提出的一个公开问题提供了肯定的答案。
In this article, we introduce and explore the notion of topological amenability in the broad setting of (locally compact) semihypergroups. We acquire several stationary, ergodic and Banach algebraic characterizations of the same in terms of convergence of certain probability measures, total variation of convolution with probability measures and translation of certain functionals, as well as the F-algebraic properties of the associated measure algebra. We further investigate the interplay between restriction of convolution product and convolution of restrictions of measures on a sub-semihypergroup. Finally, we discuss and characterize topological amenability of sub-semihypergroups in terms of certain invariance properties attained on the corresponding measure algebra of the parent semihypergroup. This in turn provides us with an affirmative answer to an open question posed by J. Wong in 1980.
