2004/05/11 by Ilwoo Cho, Cho, Ilwoo
Computer Science · Decision Sciences · Mathematics · #47-xx #Advanced Algebra and Logic #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Probability and Risk Models #Random Matrices and Applications #math.FA #math.OA #msc:47-xx
paper · pdf · doi:10.48550/arxiv.math/0405193
49 pages
arxiv created 2004/05/11 · openalex publication_date 2004/05/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In [9], we observed Amalgamated R-transform Theory. Different from the original definition of Voiculescu and Speicher, we define R-transforms of operator-valued random variable(s) by operator-valued formal series. By doing that we can establish Amalgamated R-transform calculus. In this paper, we will concentrate on observing R-transforms on a tower of amalgamated noncommutative probability spaces. We will consider the R-transform calculus and relation between R-transforms on the tower and distributions with respect to the tower. As application, we will observe the compatibility of the given tower and commuting ladders of amalgamated noncommutative probability spaces