# Multilinear function series in conditionally free probability with amalgamation

@article{Popa2007MultilinearFS,
title={Multilinear function series in conditionally free probability with amalgamation},
author={Mihai Popa},
journal={arXiv: Operator Algebras},
year={2007}
}
• M. Popa
• Published 31 March 2007
• Mathematics
• arXiv: Operator Algebras
As in the cases of freeness and monotonic independence, the notion of conditional freeness is meaningful when complex-valued states are replaced by positive conditional expectations. In this framework, the paper presents several positivity results, a version of the central limit theorem and an analogue of the conditionally free R-transform constructed by means of multilinear function series.
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## References

SHOWING 1-10 OF 11 REFERENCES

• Mathematics
• 1994
We introduce the notion of a conditionally free product and conditionally free convolution. We describe this convolution both from a combinatorial point of view, by showing its connection with the
Preliminaries on non-crossing partitions Operator-valued multiplicative functions on the lattice of non-crossing partitions Amalgamated free products Operator-valued free probability theory
• Mathematics
• 2006
Part I. Basic Concepts: 1. Non-commutative probability spaces and distributions 2. A case study of non-normal distribution 3. C*-probability spaces 4. Non-commutative joint distributions 5.
1. Modules 2. Multipliers and morphisms 3. Projections and unitaries 4. Tensor products 5. The KSGNS construction 6. Stabilisation or absorption 7. Full modules, Morita equivalence 8. Slice maps and
The notion of monotonic independence, introduced by N. Muraki, is considered in a more general frame, similar to the construction of operator-valued free probability. The paper presents constructions