ISSN:
1572-9036
Keywords:
W*-algebras
;
positive linear forms
;
Bures distance
;
inner operations
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract On a W*-algebra M, for given two positive linear forms ν,ρ∈ M + * and algebra elements a, b ∈ M, a variational expression for the Bures distance d B(ν a , ϱ b ) between the inner derived positive linear forms ν a =ν(a *·a) and ρ b =ρ(b *·b) is obtained. Along with the proof of the formula, also an earlier result of S. Gudder on noncommutative probability will be slighly extended. Also, the given expression of the Bures distance relates nicely to the system of seminorms proposed by D. Buchholz which occurs, along with the problem of estimating the so-called `weak intertwiners", in algebraic quantum field theory. In the last section, some optimization problem will be considered.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1006317508252
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