Lajos Molnár (SZTE and Rényi): Isomorphisms of positive cones in operator algebras with respect to geometric means

In this talk we are concerned with the descriptions of bijective maps between the positive definite cones in operator algebras that preserve different sorts of geometric means. We mainly focus on the Kubo-Ando geometric mean and the Fiedler-Pták geometric mean. As for the former one, we extend our existing result from the case of von Neumann factors to the case of more general algebras. As for the Fiedler-Pták geometric mean, we present the first satisfactory result that concerns the setting of finite factor von Neumann algebras.