Unital positive Schur multipliers on $S_n^p$ with a completely isometric dilation

Abstract

Let $1<p\ne 2<\infty$ and let $S_n^p$ be the associated Schatten von Neumann class over $n\times n$ matrices. We prove new characterizations of unital positive Schur multipliers $S_n^p\to S_n^p$ which can be dilated into an invertible complete isometry acting on a non-commutative $L^p$-space. Then we investigate the infinite dimensional case.

References in corpus (2)

• Dilations and rigid factorisations on noncommutative L^p-spaces
• A characterization of absolutely dilatable Schur multipliers