arXiv subjects

Dan-Virgil Voiculescu

Publications and source records attributed to Dan-Virgil Voiculescu.

22 records · Page 2Linked to original sources

arXiv2013

Free Probability for Pairs of Faces II: 2-Variables Bi-free $R$-Transform and Systems with Rank $\le 1$ Commutation

We compute the generating series for the simplest class of bi-free cumulants, beyond free cumulants, the two-bands bi-free cumulants of a pair of a left and a right variable. We also consider two-faced systems with a commutation condition implying that two-bands moments, that is expectation values of the product of a monomial of left and a monomial of right variables determine the other moments. Examples include hyponormal operators, dual systems in free entropy theory and bi-partite systems.

math.OA↗

arXiv2013

Free Probability for Pairs of Faces I

We consider a notion of bi-freeness for systems of non-commutative random variables with two faces, one of left variables and another of right variables. This includes bi-free convolution operations, bi-free cumulants and the bi-free central limit.

math.OA↗

arXiv2011

Almost normal operators mod Hilbert-Schmidt and the K-theory of the Banach algebras $EΛ(Ω)$

Is there a mod Hilbert-Schmidt analogue of the BDF-theorem, with the Pincus g-function playing the role of the index ? We show that part of the question is about the K-theory of certain Banach algebras. These Banach algebras, related to Lipschitz functions and dirichlet algebras have nice Banach space duality properties. Moreover their corona algebras are C*-algebras.

math.OA↗

arXiv2009

Free Analysis Questions II: The Grassmannian Completion and The Series Expansions at the Origin

The fully matricial generalization in part I, of the difference quotient derivation on holomorphic functions, in which ${\mathbb C}$ is replaced by a Banach algebra $B$, is extended from the affine case to a Grassmannian completion. The infinitesimal bialgebra duality, the duality transform generalizing the Stieltjes transform and the spectral theory with non-commuting scalars all extend to this completion. The series expansions of fully matricial analytic functions are characterized, providing a new way to generate fully matricial functions.

math.OA↗