Multipliers of Imprimitivity Bimodules and Morita Equivalence of Crossed Products.
Multipliers of JS-Algebras.
Multipliers on Banach algebras
Multipliers, self-induced and dual Banach algebras [Book]
Murphy's "Positive definite kernels and Hilbert C*-modules" reorganized
The paper the title refers to is that in Proceedings of the Edinburgh Mathematical Society, 40 (1997), 367-374. Taking it as an excuse we intend to realize a twofold purpose: 1° to atomize that important result showing by the way connections which are out of favour, 2° to rectify a tiny piece of history. The objective 1° is going to be achieved by adopting means adequate to goals; it is of great gravity and this is just Mathematics. The other, 2°, comes...
Mutations of C*-algebras and quasiassociative JB*-algebras
New Examples of Convolutions and Non-Commutative Central Limit Theorems
A family of transformations on the set of all probability measures on the real line is introduced, which makes it possible to define new examples of convolutions. The associated central limit theorems are studied, and examples of the limit measures, related to the classical, free and boolean convolutions, are shown.
New limit theorems related to free multiplicative convolution
Let ⊞, ⊠, and ⊎ be the free additive, free multiplicative, and boolean additive convolutions, respectively. For a probability measure μ on [0,∞) with finite second moment, we find a scaling limit of as N goes to infinity. The -transform of its limit distribution can be represented by Lambert’s W-function. From this, we deduce that the limiting distribution is freely infinitely divisible, like the lognormal distribution in the classical case. We also show a similar limit theorem by replacing free...
New scaling of Itzykson–Zuber integrals
Nice connecting paths in connected components of sets of algebraic elements in a Banach algebra
Generalizing earlier results about the set of idempotents in a Banach algebra, or of self-adjoint idempotents in a -algebra, we announce constructions of nice connecting paths in the connected components of the set of elements in a Banach algebra, or of self-adjoint elements in a -algebra, that satisfy a given polynomial equation, without multiple roots. In particular, we prove that in the Banach algebra case every such non-central element lies on a complex line, all of whose points satisfy the...
Nombres de Betti et facteurs de type
Damien Gaboriau a montré récemment que les nombres de Betti des feuilletages mesurés à feuilles contractiles sont des invariants de la relation d’équivalence associée. Sorin Popa a utilisé ce résultat joint à des propriétés de rigidité des facteurs de type II pour en déduire l’existence de facteurs de type II dont le groupe fondamental est trivial.
Non Commutative Integration for Monotone Sequentially Closed C* Algebras.
Nonclassical stochastic flows and continuous products.
Noncommutative 3-sphere as an example of noncommutative contact algebras
The notion of deformation quantization was introduced by F.Bayen, M.Flato et al. in [1]. The basic idea is to formally deform the pointwise commutative multiplication in the space of smooth functions on a symplectic manifold to a noncommutative associative multiplication, whose first order commutator is proportional to the Poisson bracket. It is of interest to compute this quantization for naturally occuring cases. In this paper, we discuss deformations of contact algebras and give a definition...
Non-Commutative Banach Function Spaces.
Noncommutative Borsuk-Ulam-type conjectures
Within the framework of free actions of compact quantum groups on unital C*-algebras, we propose two conjectures. The first one states that, if is a free coaction of the C*-algebra H of a non-trivial compact quantum group on a unital C*-algebra A, then there is no H-equivariant *-homomorphism from A to the equivariant join C*-algebra . For A being the C*-algebra of continuous functions on a sphere with the antipodal coaction of the C*-algebra of functions on ℤ/2ℤ, we recover the celebrated Borsuk-Ulam...
Noncommutative Cartan subalgebras of C*-algebras.
Non-commutative differential geometry
Non-commutative entropy computations for continuous fields and cross-products
We present here two non-commutative situations where dynamical entropy estimates are possible. The first result is concerned with automorphisms of cross-products by an exact group that commute with the group action and generalizes the result known for amenable groups. The second is about continuous fields of C-algebras and -automorphisms. Each result relies on explicit factorization via matrices.
Noncommutative extensions of the Fourier transform and its logarithm
We introduce noncommutative extensions of the Fourier transform of probability measures and its logarithm to the algebra (S) of complex-valued functions on the free semigroup S = FS(z,w) on two generators. First, to given probability measures μ, ν with all moments finite, we associate states μ̂, ν̂ on the unital free *-bialgebra (ℬ,ε,Δ) on two self-adjoint generators X,X’ and a projection P. Then we introduce and study cumulants which are additive under the convolution μ̂* ν̂ = μ̂ ⊗ ν̂ ∘ Δ when...