Speaker: Mihai Popa
Affiliation: Indiana University
Title: On c-free probability with amalgamation.
Time and Place: Thursday, April 5, 3:00-3:50pm, Milner 317.
Abstract: The notion of conditional freeness (or, shortly, c-freeness) was developed in the '90's by R. Speicher and M. Bozejko as an extension of freeness within the framework of *-algebras endowed with not one, but two states. As in the case of free probability, many of the properties of the construction are preserved if the states are replaced by positive functionals valued in a C*-algebra. We will present several positivity results, a version of the central limit theorem, the connection to monotonic independence with respect to an operator-valued functional and an analogue of the conditionally free R-transform will be constructed by means of multilinear function series.