Zobrazeno 1 - 10
of 147
pro vyhledávání: '"Voiculescu, Dan"'
Autor:
Voiculescu, Dan-Virgil
We introduced the quasicentral modulus to study normed ideal perturbations of operators. It is a limit of condenser quasicentral moduli in view of a recently noticed analogy with capacity in nonlinear potential theory. We prove here some basic proper
Externí odkaz:
http://arxiv.org/abs/2109.07633
Autor:
Voiculescu, Dan-Virgil
We point out that the quasicentral modulus is a noncommutative analogue of a nonlinear rearrangement invariant Sobolev condenser capacity. In the case of the shifts by the generators of a finitely generated group, the quasicentral modulus coincides w
Externí odkaz:
http://arxiv.org/abs/2107.11924
Autor:
Voiculescu, Dan-Virgil
We define commutants mod normed ideals associated with compact smooth manifolds with boundary. The results about the K-theory of these operator algebras include an exact sequence for the connected sum of manifolds, derived from the Mayer-Vietoris seq
Externí odkaz:
http://arxiv.org/abs/2008.06990
Autor:
Voiculescu, Dan-Virgil
We prove a general ampliation homogeneity result for the quasicentral modulus of an n-tuple of operators with respect to the (p,1) Lorentz normed ideal. We use this to prove a formula involving Hausdorff measure for the quasicentral modulus of n-tupl
Externí odkaz:
http://arxiv.org/abs/2006.14456
Autor:
Voiculescu, Dan-Virgil
We extend to the case of a threshold ideal our result with J. Bourgain about the essential centre of the commutant mod a diagonalization ideal for a n-tuple of commuting Hermitian operators . We also compute the $K_0$-group of the commutant mod trace
Externí odkaz:
http://arxiv.org/abs/1911.07377
Autor:
Voiculescu, Dan-Virgil
For the free probability analogue of Euclidean space endowed with the Gaussian measure we apply the approach of Arnold to derive Euler equations for a Lie algebra of non-commutative vector fields which preserve a certain trace. We extend the equation
Externí odkaz:
http://arxiv.org/abs/1902.02442
Autor:
Voiculescu, Dan-Virgil
We survey the operator algebras arising as commutants modulo normed ideals of finite sets of hermitian operators and connections to perturbations of operators and noncommutative geometry.
Comment: 25 pages, corrected a few typos
Comment: 25 pages, corrected a few typos
Externí odkaz:
http://arxiv.org/abs/1810.12497
Autor:
Voiculescu, Dan-Virgil
We prove a general weak existence theorem for wave operators for hybrid normed ideal perturbations. We then use this result to prove the invariance of Lebesgue absolutely continuous parts of n-tuples of commuting hermitian operators under hybrid norm
Externí odkaz:
http://arxiv.org/abs/1801.00490
We study the max-convolution and max-stable laws for Boolean independence and prove that these are Dagum distributions (also known as log-logistical distributions).
Comment: 8 pages minor corrections and improvements
Comment: 8 pages minor corrections and improvements
Externí odkaz:
http://arxiv.org/abs/1711.06227
Autor:
Voiculescu, Dan-Virgil
In hybrid normed ideal perturbations of $n$-tuples of operators, the normed ideal is allowed to vary with the component operators. We begin extending to this setting the machinery we developed for normed ideal perturbations based on the modulus of qu
Externí odkaz:
http://arxiv.org/abs/1711.05883