# مقاله Abstract structure of partial function $*$-algebras over semi-direct product of locally compact groups

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مقاله Abstract structure of partial function $*$-algebras over semi-direct product of locally compact groups دارای 33 صفحه می باشد و دارای تنظیمات در microsoft word می باشد و آماده پرینت یا چاپ است

فایل ورد مقاله Abstract structure of partial function $*$-algebras over semi-direct product of locally compact groups  کاملا فرمت بندی و تنظیم شده در استاندارد دانشگاه  و مراکز دولتی می باشد.

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## بخشی از متن مقاله Abstract structure of partial function $*$-algebras over semi-direct product of locally compact groups :

سال انتشار : 2015

تعداد صفحات :33

This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $\tau:H\to Aut(K)$ be a continuous homomorphism. Let $G_\tau=H\ltimes_\tau K$ be the semi-direct product of $H$ and $K$ with respect to $\tau$. We define left and right $\tau$-convolution on $L^1(G_\tau)$ and we show that, with respect to each of them, the function space $L^1(G_\tau)$ is a Banach algebra. We define $\tau$-convolution as a linear combination of the left and right $\tau$-convolution and we show that the $\tau$-convolution is commutative if and only if $K$ is abelian. We prove that there is a $\tau$-involution on $L^1(G_\tau)$ such that with respect to the $\tau$-involution and $\tau$-convolution, $L^1(G_\tau)$ is a non-associative Banach $*$-algebra. It is also shown that when $K$ is abelian, the $\tau$-involution and $\tau$-convolution make $L^1(G_\tau)$ into a Jordan Banach $*$-algebra. Finally, we also present the generalized notation of $\tau$-convolution for other $L^p$-spaces with $p>1$.

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