Hypergroups and invariant complemented subspaces

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• 作者：Nazanin Tahmasebi ^{ntahmase@ualberta.ca" class="auth_mail}
• 关键词：Hypergroup ; Invariant mean ; Weil subhypergroup ; Translation invariant complemented subspace ; Folner type growth property ; Weakly almost periodic ; Left translation invariant C鈦?/sup>C鈦?/mo>-subalgebra ; Compact subhypergroup ; Amenability
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：15 June, 2014
• 年：2014
• 卷：414
• 期：2
• 页码：641-655
• 全文大小：355 K

文摘

Let K be a hypergroup with a Haar measure. The purpose of the present paper is to initiate a systematic approach to the study of the class of invariant complemented subspaces of and , the class of left translation invariant -subalgebras of and finally the class of non-zero left translation invariant -subalgebras of in the hypergroup context with the goal of finding some relations between these function spaces. Among other results, we construct two correspondences: one, between closed Weil subhypergroups and certain left translation invariant -subalgebras of , and another, between compact subhypergroups and a specific subclass of the class of left translation invariant -subalgebras of . By the help of these two characterizations, we extract some results about invariant complemented subspaces of and .