Compatibility of a noncommutative probability space and a noncommutative probability space with amalgamation

Details Compatibility of a noncommutative probability space and a noncommutative probability space with amalgamation Compatibility of a noncommutative probability space and a noncommutative probability space with amalgamation

2004-05-11

arxiv.org/abs/math/0405192v2

Mathematics

Operator Algebras

37 pages

Scientific paper

In this paper, we will consider R-transform theory and R-transform calculus for compatible noncommutative probability space and amagamated noncommutative probability space. By doing this, we can realize the relation between scalar-valued R-transforms and operator-valued moment series, under the compatibility. Also, we can see that there is a big gap between freeness and amalgamated freeness.

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