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- W4287641574 abstract "Every homomorphism $varphi: B(G) rightarrow B(H)$ between Fourier-Stieltjes algebras on locally compact groups $G$ and $H$ is determined by a continuous mapping $alpha: Y rightarrow Delta(B(G))$, where $Y$ is a set in the open coset ring of $H$ and $Delta(B(G))$ is the Gelfand spectrum of $B(G)$ (a $*$-semigroup). We exhibit a large collection of maps $alpha$ for which $varphi=j_alpha: B(G) rightarrow B(H)$ 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 $varphi: B(G) rightarrow B(H)$ 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." @default.
- W4287641574 created "2022-07-25" @default.
- W4287641574 creator A5045467460 @default.
- W4287641574 date "2020-10-13" @default.
- W4287641574 modified "2023-10-17" @default.
- W4287641574 title "Homomorphisms of Fourier-Stieltjes algebras" @default.
- W4287641574 doi "https://doi.org/10.48550/arxiv.2010.06650" @default.
- W4287641574 hasPublicationYear "2020" @default.
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