Approximate double commutants in von Neumann algebras
classification
🧮 math.OA
math.FA
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neumannalgebradoubleapproximatecommutantcommutativeeveryrelative
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Richard Kadison showed that not every commutative von Neumann subalgebra of a factor von Neumann algebra is equal to its relative double commutant. We prove that every commutative C*-subalgebra of a centrally prime C*-algebra $B$ equals its relative approximate double commutant. If $B$ is a von Neumann algebra, there is a related distance formula.
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