On Bures Distance and-Algebraic Transition Probability between Inner Derived Positive Linear Forms over W-Algebras

摘要: On a W*-algebra M, for given two positive linear forms ν,ρ∈ M + * and algebra elements a, b ∈ variational expression the Bures distance d B(ν a , ϱ b ) between inner derived ν =ν(a *·a) ρ =ρ(b *·b) is obtained. Along with proof of formula, also an earlier result S. Gudder on noncommutative probability will be slighly extended. Also, relates nicely to system seminorms proposed by D. Buchholz which occurs, along problem estimating so-called `weak intertwiners", in algebraic quantum field theory. In last section, some optimization considered.