Isometric isomorphisms of Beurling algebras

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• 作者：Safoura Zadeh ^{jsafoora@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Locally compact groups ; Beurling algebras ; Isometric isomorphisms ; Arens product
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 June 2016
• 年：2016
• 卷：438
• 期：1
• 页码：1-13
• 全文大小：377 K

文摘

Let G and H   be locally compact groups with continuous weights ω₁${\omega }_1$ and ω₂${\omega }_2$ respectively, such that 0f25365bb9e34911ac8d6782dee" title="Click to view the MathML source">ω_i(e_i)=1${\omega }_i(e_i)=1$, i=1,2$i=1,2$. In this article we show that if M(G,ω₁)$M(G,{\omega }_1)$ (the weighted measure algebra on G  ) is isometrically algebra isomorphic to M(H,ω₂)$M(H,{\omega }_2)$, then the underlying weighted groups are isomorphic, i.e. there exists an isomorphism of topological groups ϕ:G→H$\varphi :G\to H$ such that $\frac{{\omega }_1}{{\omega }_2\circ \varphi }$ is multiplicative. Similarly, we show that any weighted locally compact group (G,ω)$(G,\omega )$ is completely determined by its Beurling group algebra 70ff3" title="Click to view the MathML source">L¹(G,ω)$L^1(G,\omega )$, LUC(G,ω⁻¹)^⁎$\mathit{LUC}{(G,{\omega }^{-1})}^{⁎}$ and L¹(G,ω)^⁎⁎$L^1{(G,\omega )}^{⁎⁎}$, when the two last algebras are equipped with an Arens product.