In this paper, the author proves an asymptotic version of the double commutant theorem, in a particular set-up of commutative C∗-algebras. More precisely, he considers the relative approximate double commutant of a C∗-algebra with unit, and, using atheorem of characterization for a commutative C∗-subalgebra with unit (inspired by awell-known result due to Kadison for a von Neumann sub-algebra of type I), and from atheorem based on a Machado result, he proves that if A is a commutative C∗-subalgebra of a C∗-algebra B centrally prime with unit, then A is equal to its relative approximatedouble commutant. In the case where B is a von Neumann algebra, a distance formula is found.
|Numero di pagine||1|
|Stato di pubblicazione||Published - 2015|