The ideal structure of the Haagerup tensor product of C*-algebras.
The index of projective families of elliptic operators.
The injective hull of an archimedean f-algebra
The intrinsic invariant of an approximately finite dimensional factor and the cocycle conjugacy of discrete amenable group actions.
The invertible elements are dense in the irrational rotation C*-algebras.
The isolated ideal of a correspondence associated with a topological quiver.
The joint approximate spectrum of a finite system of elements of a C*-algebra
The Kadec-Pełczyński-Rosenthal subsequence splitting lemma for JBW*-triple preduals
Any bounded sequence in an L¹-space admits a subsequence which can be written as the sum of a sequence of pairwise disjoint elements and a sequence which forms a uniformly integrable or equiintegrable (equivalently, a relatively weakly compact) set. This is known as the Kadec-Pełczyński-Rosenthal subsequence splitting lemma and has been generalized to preduals of von Neuman algebras and of JBW*-algebras. In this note we generalize it to JBW*-triple preduals.
The Kolmogorov Entropy For Quantum Systems Revisited.
The K-theory of abelian subalgebras of AF algebras.
The K-theory of the triple-Toeplitz deformation of the complex projective plane
, i,j ∈ 1,2,3, i ≠ j, of C*-epimorphisms assuming that it satisfies the cocycle condition. Then we show how to compute the K-groups of the multi-pullback C*-algebra of such a family, and exemplify it in the case of the triple-Toeplitz deformation of ℂP².
The Lévy-Khintchine formula and Nica-Speicher property for deformations of the free convolution
We study deformations of the free convolution arising via invertible transformations of probability measures on the real line T:μ ↦ Tμ. We define new associative convolutions of measures by . We discuss infinite divisibility with respect to these convolutions, and we establish a Lévy-Khintchine formula. We conclude the paper by proving that for any such deformation of free probability all probability measures μ have the Nica-Speicher property, that is, one can find their convolution power for...
The Lie structure of C* and Poisson algebras
The Linear Groups of Injective Factors and of Matroid C*Algebras are Contractible to a Point.
The Local Index Formula in Noncommutative Geometry.
The maximum unitary rank of some C*-algebras.
The Mayer-Vietoris and the Puppe sequences in K-theory for C*-algebras
The microstates free entropy dimension of any DT--operator is 2.
The minimal dense two-sided ideal of a C*-algebra with continous trace.
The monotone cumulants
In the present paper we define the notion of generalized cumulants which gives a universal framework for commutative, free, Boolean and especially, monotone probability theories. The uniqueness of generalized cumulants holds for each independence, and hence, generalized cumulants are equal to the usual cumulants in the commutative, free and Boolean cases. The way we define (generalized) cumulants needs neither partition lattices nor generating functions and then will give a new viewpoint to cumulants....