可服从拟格序群与真表示

IF 0.4 Q4 MATHEMATICS Boletim Sociedade Paranaense de Matematica Pub Date : 2022-12-27 DOI:10.5269/bspm.62552
M-Alamin A. H. Ahmed
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引用次数: 0

摘要

设(G,P)是一个拟格序群。在[2]中,我们构造了(G,P)的通用协变表示(a,U),避免了[11]和[8]中其他方法的一些复杂性。然后我们证明了如果(G,P)是可服从的,则(G,P)的真表示生成C*-代数,其与由泛协变表示生成的C*-代规范同构。在本文中,我们以一种相对简单和自然的方式讨论了可适性的特征,以引入这一强大的性质。(G,P)的可修性可以通过研究ΦU在正的、忠实的线性映射的范围上的行为而不是整个代数上的行为来建立。
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Amenable quase-lattice ordered groups and true representations
Let (G, P) be a quasi-lattice ordered group. In [2] we constructed a universal covariant representation (A,U) for (G, P) in a way that avoids some of the intricacies of the other approaches in [11] and [8]. Then we showed if (G, P) is amenable, true representations of (G, P) generate C∗-algebras which are canonically isomorphic to the C∗-algebra generated by the universal covariant representation. In this paper, we discuss characterizations of amenability in a comparatively simple and natural way to introduce this formidable property. Amenability of (G, P) can be established by investigating the behavior of ΦU on the range of a positive, faithful, linear map rather than the whole algebra.
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
140
审稿时长
25 weeks
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