Diagonalizing matrices over AW*-algebras
classification
🧮 math.OA
keywords
algebrasmatricesalgebracategorycommutingconsequencedevelopeddiagonalized
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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.
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