A bipolar property of subgroups and translation invariant closed convex subsets

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:388

Article

Cheng, Michael Yin-Hei

关键词: Locally compact groups;    Non-commutative abstract harmonic analysis;    Dual spaces;    Closed convex subsets;   

DOI  :  10.1016/j.jmaa.2011.10.041

来源: Elsevier

【 摘 要 】

Let G be a locally compact group. We define the bipolar property of subgroups of G using the concept of the dual space G* and show that a subgroup H has the bipolar property if and only if G had H-separation property. We study generalized translation invariant closed convex subset of A(G) and VN(G). We also prove that every completely complemented weak*-closed translation invariant subspace of VN(G) is invariantly complemented if G is amenable and give characterizations of WAP((G) over cap) and AP((G) over cap) by using the generalized translation via elements in G*. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free