English

R-transform Theory On a Tower of Amalgamated Noncommutative Probability Spaces

Operator Algebras 2007-05-23 v1 Functional Analysis

Abstract

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

Keywords

Cite

@article{arxiv.math/0405193,
  title  = {R-transform Theory On a Tower of Amalgamated Noncommutative Probability Spaces},
  author = {Ilwoo Cho},
  journal= {arXiv preprint arXiv:math/0405193},
  year   = {2007}
}

Comments

49 pages

R2 v1 2026-07-22T17:05:19.962Z