# 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} }

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.

## 8 Citations

### Appell polynomials and their relatives III. Conditionally free theory

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We extend to the multivariate non-commutative context the descriptions of a "once-stripped" probability measure in terms of Jacobi parameters, orthogonal polynomials, and the moment generating…

### On the multiplication of operator-valued c-free random variables

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We discuss some results concerning the multiplication of non-commutative random variables that are c-free with respect to a pair $( \Phi, \varphi) $, where $ \Phi $ is a linear map with values in…

### A NOTE ON AMALGAMATED MONOTONE, ANTI-MONOTONE, AND ORDERED-FREE PRODUCTS OF OPERATOR-VALUED QUANTUM PROBABILITY SPACES

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We directly prove that the amalgamated monotone or anti-monotone products (in N. Muraki’s originary sense [17], for the scalar-valued case) (see also M. Popa’s paper [22], for an operator-valued…

### A Fock space model for addition and multiplication of c-free random variables

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The paper presents a Fock space model suitable for constructions of c-free algebras. Immediate applications are direct proofs for the properties of the c-free R- and S-transforms.

### Conditionally Bi-Free Independence with Amalgamation

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In this paper, we introduce the notion of conditionally bi-free independence in an amalgamated setting. We define operator-valued conditionally bi-multiplicative pairs of functions and construct…

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