Title: A simple proof of Størmer’s theorem
Speaker: Stanislaw Szarek (Kerr Professor of Mathematics, Case Western Reserve University)
Abstract: The structure of the set of positivity-preserving maps between matrix algebras is notoriously difficult to describe. The notable exceptions are the low dimensional cases settled by Størmer and Woronowicz, which assert that every such map is a sum of finite number of maps of the form X -> AXA* and X -> A(X^T)A*, where ^T is the transpose and * is the Hermitian conjugate. However, even in these cases the previous arguments (known to the speaker) were based on long and seemingly ad hoc computations. We show a simple proof – based on Brouwer’s fixed point theorem – for the 2 x 2 case (Størmer’s theorem).