论文标题
与本地紧凑型组上与傅立叶代数有关的一些Banach代数的几何特性
Geometric Properties of some Banach Algebras related to the Fourier algebra on Locally Compact Groups
论文作者
论文摘要
令$ a_p（g）$表示本地紧凑型组的figa-talamanca-herz banach代数}} $ g $，因此$ a_2（g）$ {\ it {是$ g $的傅立叶代数。如果$ g $是交换的，则$ a_2（g）= l^1（\ hat {g}）^\ wedge $。让$ a_p^r（g）= a_p \ cap l^r（g）$，带有norm $ \ | | u \ | _ {a_p^r} = \ | u \ | _ {a_p}+\ | u \ | _ {l^r} $。我们研究了哪个$ p $，$ r $和$ g $做Banach代数$ a_p^r（g）$ {\ it {拥有Banach空间几何属性：Radon-Nikodym properties（RNP），Schur Property（sp）或Dunford-Pettis属性（dunford-petp）。即使$ g = r $（实际行）或$ g = z $（添加剂整数），结果也是新的。
Let $A_p(G)$ denote the Figa-Talamanca-Herz Banach Algebra of the locally compact group}} $G$, thus $A_2(G)$ {\it{is the Fourier Algebra of $G$. If $G$ is commutative then $A_2(G)=L^1(\hat{G})^\wedge$. Let $A_p^r(G)=A_p\cap L^r(G)$ with norm $\|u\|_{A_p^r}=\| u\|_{A_p}+\| u\|_{L^r}$.We investigate for which $p$, $r$, and $G$ do the Banach algebras $A_p^r(G)$ {\it{have the Banach space geometric properties: The Radon-Nikodym Property (RNP), the Schur Property (SP) or the Dunford-Pettis Property (DPP). The results are new even if $G=R$ (the real line) or $G=Z$ (the additive integers).
