论文标题
傅里叶式代数的同态
Homomorphisms of Fourier-Stieltjes algebras
论文作者
论文摘要
每个同构$φ：b（g）\ rightarrow b（h）$之间的傅立叶 - stieltjes代数之间本地紧凑型组的代数$ g $和$ h $确定由连续的映射$α：y \rightarrowΔ（y \rightarrowΔ（b（g））$，$ y $，$ y $是$ h $ h $ h $ h $ h $ h $和$ h $ g（b）（b）（b $ h $ g（b）（b）（b）（b） $ b（g）$（$*$ - 半群）。我们展示了大量的地图$α$，其中$φ=j_α：b（g）\ rightarrow b（h）$是一种完全积极/完全承诺/完全有限的同构，并在多种情况下建立相反的语句。例如，当$ g $是欧几里得 - 或$ p $ -Adic-Motion Group时，我们完全表征所有完全表征所有完全积极/完全有限/完全有限的同构$φ：b（g）\ rightarrow b（h）$。在这些情况下，我们对完全积极/完全合同的同态的描述采用了“同构/仿射图兼容系统的融合图”的概念，并且与傅立叶代数情况大不相同。
Every homomorphism $φ: B(G) \rightarrow B(H)$ between Fourier-Stieltjes algebras on locally compact groups $G$ and $H$ is determined by a continuous mapping $α: Y \rightarrow Δ(B(G))$, where $Y$ is a set in the open coset ring of $H$ and $Δ(B(G))$ is the Gelfand spectrum of $B(G)$ (a $*$-semigroup). We exhibit a large collection of maps $α$ for which $φ=j_α: B(G) \rightarrow B(H)$ is a completely positive/completely contractive/completely bounded homomorphism and establish converse statements in several instances. For example, we fully characterize all completely positive/completely contractive/completely bounded homomorphisms $φ: B(G) \rightarrow B(H)$ when $G$ is a Euclidean- or $p$-adic-motion group. In these cases, our description of the completely positive/completely contractive homomorphisms employs the notion of a "fusion map of a compatible system of homomorphisms/affine maps" and is quite different from the Fourier algebra situation.
