论文标题
重新审视傅里叶代数的完全有限的同构
Completely bounded homomorphisms of the Fourier algebra revisited
论文作者
论文摘要
令$ a（g）$和$ b（h）$是本地紧凑型组$ g $和$ h $的傅立叶和傅立叶代数。 Ilie和Spronk表明，连续的分段仿射地图$α：y \ subseteq h \ rightarrow g $诱导完全有限的同构$φ$φ：a（g）\ rightarrow b（h）$，当$ g $是$ g $时，每种完全有限的同源性都会以这种方式出现。科恩（Cohen）在阿贝里安（Abelian）环境中的这项广义工作。我们认为，现有论点的关键引理存在差距，我们看不到如何修复。我们在这里提出了一种不同的策略来展示结果，而不是使用拓扑论点，而是更加合并，并利用衡量理论思想，更紧密地遵循了科恩的原始思想。
Let $A(G)$ and $B(H)$ be the Fourier and Fourier-Stieltjes algebras of locally compact groups $G$ and $H$, respectively. Ilie and Spronk have shown that continuous piecewise affine maps $α: Y \subseteq H\rightarrow G$ induce completely bounded homomorphisms $Φ:A(G)\rightarrow B(H)$, and that when $G$ is amenable, every completely bounded homomorphism arises in this way. This generalised work of Cohen in the abelian setting. We believe that there is a gap in a key lemma of the existing argument, which we do not see how to repair. We present here a different strategy to show the result, which instead of using topological arguments, is more combinatorial and makes use of measure theoretic ideas, following more closely the original ideas of Cohen.
