Orthogonal ${\ell }_1$-sets and extreme non-Arens regularity of preduals of von Neumann algebras

Mahmoud Filali, Jorge Galindo

We propose a new definition for a Banach algebra $\mathfrak{A}$ to be extremely non-Arens regular, namely that the quotient ${\mathfrak{A}}^{\ast }/\mathcal{WAP}(\mathfrak{A})$ of $\mat…