The strong law of large numbers for states and traces of aW*-algebra
The strong law of large numbers for states and traces of aW*-algebra
Let $$\mathfrak{A}$$ be aW*-algebra with faithful normal stateρ. Several different notions of independence with respect toρ are introduced for operators in $$\mathfrak{A}$$ . A non-commutative extension of the strong law of large numbers is proved. Whenρ is a trace, this theorem is extended to cover unbounded operators associated withA.