2018/05/03 by Öztop, Serap, Samei, Ebrahim, Shepelska, Varvara
#43A15 #43A20 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary 46E30 #Secondary 20J06
paper · doi:10.48550/arxiv.1805.02503
Let G be a locally compact group, let Ω:G× G→ ℂ be a 2-cocycle, and let (Φ,Ψ) be a complementary pair of strictly increasing continuous Young functions. It is shown in \citeOS2 that (LΦ(G),\circledast) becomes an Arens regular dual Banach algebra if |Ω(s,t)|≤ u(s)+v(t) (s,t∈ G) for some u,v∈ SΨ(G). We prove if LΦ(G)⊆ L2(G) and u,v can be chosen to belong to L2(G), then (LΦ(G),\circledast) with the maximal operator space structure is completely isomorphic to an operator algebra. We also present further classes of 2-cocycles for which one could obtain such algebras generalizing in part the results of \citeOS1. We apply our methods to compactly generated group of polynomial growth and demonstrate that our results could be applied to variety of cases.