W ~*-代数上内导正线性型之间的Bures-距离和~*-代数转移概率
On Bures-Distance and *-Algebraic Transition Probability between Inner Derived Positive Linear Forms over W*-Algebra
摘要：
在W*-代数M上，对于给定的两个正线性形式f，g和代数元a，b，给出了内导正线性形式f^a=f（a* . a）和g^b=g（b* . b）得到。随着公式的证明，S.Gudder关于非交换概率的一些早期结果也将被稍微推广。此外，给出的布勒斯距离的表达式很好地与D.Buchholz提出的一些规范系统有关，这些规范系统是在估计代数量子场论中所谓的“弱缠绕”问题时出现的。在最后一部分，一些优化问题将被考虑。
英文摘要：
On a W*-algebra M, for given two positive linear forms f,g and algebra elements a,b a variational expression for the Bures-distance d_B(f^a,g^b) between the inner derived positive linear forms f^a=f(a* . a) and g^b=g(b* . b) is obtained. Along with the proof of the formula also some earlier result of S.Gudder on non-commutative probability will be slightly extended. Also, the given expression of the Bures-distance nicely relates to some system of seminorms proposed by D.Buchholz and which occured along with the problem of estimating the so-called `weak intertwiners' in algebraic quantum field theory. In the last part some optimization problem will be considered.
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