2020/06/01 by Mahmoud Filali, Filali, Mahmoud, Jorge Galindo +1
Mathematics · #22D15 #43A46 #43A60 #47C15 #47D35 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2006.00851
openalex publication_date 2020/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new definition for a Banach algebra \mathfrakA to be extremely non-Arens regular, namely that the quotient \mathfrakA^∗/\mathscrWAP(\mathfrakA) of \mathfrakA^∗ with the space of its weakly almost periodic elements contains an isomorphic copy of \mathfrakA^∗. This definition is simpler and formally stronger than the original one introduced by Granirer in the nineties. We then identify sufficient conditions for the predual \mathfrakV_∗ of a von Neumann algebra \mathfrakV to be extremely non-Arens regular in this new sense. These conditions are obtained with the help of orthogonal ℓ1-sets of \mathfrakV_∗. We show that some of the main algebras in Harmonic Analysis satisfy these conditions. Among them,there is \small \bullet the weighted semigroup algebra of any weakly cancellative discrete semigroup, for any diagonally bounded weight, \small \bullet the weighted group algebra of any non-discrete locally compact infinite group and for any weight, \small \bullet the weighted measure algebra of any locally compact infinite group, for any diagonally bounded weight, \small \bullet the Fourier algebra of any locally compact infinite group having its local weight greater or equal than its compact covering number, \small \bullet the Fourier algebra of any countable discrete group containing an infinite amenable subgroup.