双测度代数的同调性质及其BSE性质
Homological propeties of Bimeasure algebras and their BSE properties
摘要：
设$G$和$H$是局部紧群. $BM(G, H)$表示$C_{0}(G)\times C_{0}(H)$上有界双线性型的巴拿赫代数，本文研究了双测度代数的同调性质.证明了双测度代数$BM(G, H)$是顺从的当且仅当$G$和$H$是离散的.评估了$BM(G, H)$和$M(G\times H)$的弱顺应性之间的相关性。证明了双测度代数$BM(G, H)$的双投射性等价于$G$和$H$的有限性.进一步证明了双测度群代数$BM_{a}(G, H)$是BSE代数.得到了$BM(G, H)$是BSE-代数的充要条件是$G$和$H$是离散群.
英文摘要：
Let $G$ and $H$ be locally compact groups. $BM(G, H)$ denoted the Banach algebra of bounded bilinear forms on $C_{0}(G)\times C_{0}(H)$.In this paper, the homological properties of Bimeasure algebras are investigated. It is found and approved that the Bimeasure algebras $BM(G, H)$ is amenable if and only if $G$ and $H$ are discrete. The correlation between the weak amenability of $BM(G, H)$ and $M(G\times H)$ is assessed. It is found and approved that the biprojectivity of the bimeasure algebra $BM(G, H)$ is equivalent to the finiteness of $G$ and $H$. Furthermore, we show that the bimeasure group algebra $BM_{a}(G, H)$ is a BSE algebra. It will be concluded that $BM(G, H)$ is a BSE- algebra if and only if $G$ and $H$ are discrete groups.
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