Diagonalizing matrices over AW*-algebras
arXiv:1208.5120 · doi:10.1016/j.jfa.2013.01.022
Abstract
Every commuting set of normal matrices with entries in an AW*-algebra can be simultaneously diagonalized. To establish this, a dimension theory for properly infinite projections in AW*-algebras is developed. As a consequence, passing to matrix rings is a functor on the category of AW*-algebras.
24 pages. Comments very welcome!