Artículos de revistas
Unitarization of uniformly bounded subgroups in finite von Neumann algebras
Fecha
2014-12Registro en:
Miglioli, Martín Carlos; Unitarization of uniformly bounded subgroups in finite von Neumann algebras; Oxford University Press; Bulletin Of The London Mathematical Society; 46; 6; 12-2014; 1264-1266
0024-6093
CONICET Digital
CONICET
Autor
Miglioli, Martín Carlos
Resumen
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.