Hypergroups and invariant complemented subspaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:414

Article

Tahmasebi, Nazanin

关键词: Hypergroup;    Invariant mean;    Weil subhypergroup;    Translation invariant complemented subspace;    Folner type growth property;    Weakly almost periodic;    Left translation invariant;    C*-subalgebra;    Compact subhypergroup;    Amenability;   

DOI  :  10.1016/j.jmaa.2014.01.026

来源: Elsevier

【 摘 要 】

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 L infinity (K) and C-0 (K), the class of left translation invariant w*-subalgebras of L,, (K) and finally the class of non-zero left translation invariant C*-subalgebras of C-0 (K) 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 Well subhypergroups and certain left translation invariant w*-subalgebras of L infinity(K), and another, between compact subhypergroups and a specific subclass of the class of left translation invariant C*-subalgebras of C-0(K). By the help of these two characterizations, we extract some results about invariant complemented subspaces of L infinity(K) and C-0 (K). (c) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free