On central limit theorems in probability gage spaces
A probability gage space over a semi-finite \(W^*\)-algebra is considered as a non-commutative or quantum analogue of the classical probability space. In this setting some limit theorems are proved and, in particular a Levy-Khinchine type of representation for the Fourier transforms of limit probability gages is established. The results are obtained by exploiting some of the algebraic and topological properties of certain set of operators called the decomposability algebraic structures, associated with probability gages. Reviewer's remark: Another approach to central limit theorems in non- commutative probability theory is given in papers of \textit{B. G. Gol'dsthejn} [e.g. Teor. Veroyatn. Primen. 27, No.4, 657-666 (1982; Zbl 0506.46048); English translation in Theory Probab. Appl. 27, 703-714 (1982)].
scientific article; zbMATH DE number 3953957