99 citations · 460 across the 54 of their papers we have counts for
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Operator-valued distributions: I. Characterizations of freeness
Alexandru Nica, Dimitri Shlyakhtenko, Roland Speicher
Let be a -probability space. Assume that itself is a -probability space; then can be viewed as -probability space as well. Let be in . We look at the qu…
Grothendieck's Theorem for Operator Spaces
Gilles Pisier, Dimitri Shlyakhtenko
We prove several versions of Grothendieck's Theorem for completely bounded linear maps , when E and F are operator spaces. We prove that if E,F are -algebra…
A Characterization of Freeness by a Factorization Property of R-transform
Alexandru Nica, Dimitri Shlyakhtenko, Roland Speicher
Let M be a B-probability space. Assume that B itself is a D-probability space; then M can be viewed as a D-probability space as well. Let X be in M. We characterize freeness of X f…
Free Fisher Information for Non-Tracial States
Dimitri Shlyakhtenko
We extend Voiculescu's microstates-free definitions of free Fisher information and free entropy to the non-tracial framework. We explain the connection between these quantities and…
R-cyclic families of matrices in free probability
Alexandru Nica, Dimitri Shlyakhtenko, Roland Speicher
We introduce the concept of ``R-cyclic family'' of matrices with entries in a non-commutative probability space; the definition consists in asking that only the ``cyclic'' non-cros…