论文标题
在$ \a_φ（g）$中的代数结构上
On the algebraic structures in $\A_Φ(G)$
论文作者
论文摘要
令$ g $为本地紧凑型组，$（φ，ψ）$为$ n $ functions的补充对。在本文中，使用强大的孔隙率工具，证明当$ g $是一个可正常的群体时，则figà-Talamanca-herz-orlicz-orlicz algebra $ {\ a}_φ（g）$是Banach代数卷积的卷积产品，并且仅在$ G $被压缩时才。然后证明$ {\ a}_φ（g）$是segal代数，结果，在卷积产品下，讨论了$ {\ a}_φ（g）$的$ {\ a}_φ（g）$，并且存在$ {\ a}_φ（g）$的有限近似身份。此外，可以证明，对于紧凑型Abelian $ g $，可以用$ \ wideHat {g} $确定$ {\ a}_φ（g）$的字符空间，$ g $。
Let $G$ be a locally compact group and $(Φ, Ψ)$ be a complementary pair of $N$-functions. In this paper, using the powerful tool of porosity, it is proved that when $G$ is an amenable group, then the Figà-Talamanca-Herz-Orlicz algebra ${\A}_Φ(G)$ is a Banach algebra under convolution product if and only if $G$ is compact. Then it is shown that ${\A}_Φ(G)$ is a Segal algebra, and as a consequence, the amenability of ${\A}_Φ(G)$ and the existence of a bounded approximate identity for ${\A}_Φ(G)$ under the convolution product is discussed. Furthermore, it is shown that for a compact abelian group $G$, the character space of ${\A}_Φ(G)$ under convolution product can be identified with $\widehat{G}$, the dual of $G$.
