Free Calculus
نویسنده
چکیده
1.1. Definitions. 1) A (non-commutative) probability space consists of a pair (A, φ), where • A is a unital algebra • φ : A → C is a unital linear functional, i.e. in particular φ(1) = 1 2) Unital subalgebras A1, . . . ,An ⊂ A are called free, if we have φ(a1 . . . ak) = 0 whenever ai ∈ Aj(i) (i = 1, . . . , k) j(1) 6= j(2) 6= · · · 6 = j(k) φ(ai) = 0 (i = 1, . . . , k) 3) Random variables x1, . . . , xn ∈ A are called free, if A1, . . . ,An are free, where Ai is the unital algebra generated by xi.
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