Unitarization of uniformly bounded subgroups in finite von Neumann algebras

MARTÍN MIGLIOLI

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY

OXFORD UNIV PRESS

Lugar: Oxford; Año: 2014

0024-6093

This note presents a new proof of the fact that every uniformly bounded group of invertible elements in a finite von Neumann algebra is similar to a unitary group. In 1974, Vasilescu and Zsido proved this result using the Ryll?Nardzewsky fixed point theorem [Vasilescu and Zsido, "Uniformly bounded groups in finite W*-algebras", Acta Sci. Math. (Szeged) 36 (1974) 189-192]. This new proof involves metric geometric arguments in the non-positively curved space of positive invertible operators of the algebra, which yield a more explicit unitarizer.