A bipolar property of subgroups and translation invariant closed convex subsets

作者：Cheng Michael Yin Hei^*

来源：Journal of Mathematical Analysis and Applications, 2012, 388(1): 160-174.

DOI：10.1016/j.jmaa.2011.10.041

• Locally compact groups
• Non-commutative abstract harmonic analysis
• Dual spaces
• Closed convex subsets

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*.

• 出版日期2012-4-1