A characterization of completely bounded normal Jordan $*$-homomorphisms on von Neumann algebras

TL;DR

This paper provides a detailed characterization of completely bounded normal Jordan $*$-homomorphisms on von Neumann algebras and explores completely positive isometries on noncommutative L^p-spaces, advancing understanding in operator algebra mappings.

Contribution

It introduces new characterizations of these homomorphisms and isometries, extending the theoretical framework of operator algebra mappings.

Findings

Characterization of completely bounded normal Jordan $*$-homomorphisms.

Description of completely positive isometries on noncommutative L^p-spaces.

Enhanced understanding of structure-preserving maps in operator algebras.

Abstract

We characterize completely bounded normal Jordan $*$-homomorphisms acting on von Neumann algebras. We also characterize completely positive isometries acting on noncommutative $\mathrm{L}^p$-spaces.