Completely positive matrix numerical index on matrix regular operator spaces (Q2845741)

The aim of this paper is to compute the completely positive matrix numerical index of matrix regular operator spaces. This is a constant relating the matrix norm and the matrix order of the space. Among other results, the author shows that the completely positive matrix numerical index of \(S_p(H)\) (the \(p\)-Schatten class space of a Hilbert space \(H\) of dimension greater than \(1\)) and \(L_p(M)\) (the non-commutative \(L_p\)-space of a finite von Neumann algebra of dimension greater than \(1\)) are \(2^{-\frac{1}{p} }\).