On the continuity of the map \(\phi\) \(\to | \phi |\) from the predual of a \(W^*\)-algebra
Let \(\phi\),\(\psi\) be elements of the predual of a \(W^*\)-algebra. Then \[ \| | \phi | -| \psi | \| \leq (2\| \phi +\psi \| \| \phi -\psi \|)^{1/2}. \] This estimate is best possible. The proof uses the theory of noncommutative \(L^ p\)-spaces.
scientific article; zbMATH DE number 3935767