Extensions des -algèbres
Extensions of certain real rank zero -algebras
G. Elliott extended the classification theory of -algebras to certain real rank zero inductive limits of subhomogeneous -algebras with one dimensional spectrum. We show that this class of -algebras is not closed under extensions. The relevant obstruction is related to the torsion subgroup of the -group. Perturbation and lifting results are provided for certain subhomogeneous -algebras.
Extensions of derivations II.
Extensions of dimension groups and AF C*-algebras.
Extensions of stable -algebras.
Extremal problems for completely positive maps.
Extreme points of the closed unit ball in C*-algebras
In this short note we give a short and elementary proof of a characterization of those extreme points of the closed unit ball in C*-algebras which are unitary. The result was originally proved by G. K. Pedersen using some methods from the theory of approximation by invertible elements.
Extreme Positive Linear Maps on C*-Algebras.
Facial structures of separable and PPT states
A positive semi-definite block matrix (a state if it is normalized) is said to be separable if it is the sum of simple tensors of positive semi-definite matrices. A state is said to be entangled if it is not separable. It is very difficult to detect the border between separable and entangled states. The PPT (positive partial transpose) criterion tells us that the partial transpose of a separable state is again positive semi-definite, as was observed by M. D. Choi in 1982 from...
Factorizing multilinear operators on Banach spaces, C*-algebras and JB*-triples
In recent papers, the Right and the Strong* topologies have been introduced and studied on general Banach spaces. We characterize different types of continuity for multilinear operators (joint, uniform, etc.) with respect to the above topologies. We also study the relations between them. Finally, in the last section, we relate the joint Strong*-to-norm continuity of a multilinear operator T defined on C*-algebras (respectively, JB*-triples) to C*-summability (respectively, JB*-triple-summability)....
Feuilletages et algèbres d'opérateurs
Finite generation in C*-algebras and Hilbert C*-modules
We characterize C*-algebras and C*-modules such that every maximal right ideal (resp. right submodule) is algebraically finitely generated. In particular, C*-algebras satisfy the Dales-Żelazko conjecture.
Finite sums and products of commutators in inductive limit -algebras
Results of T. Fack, P. de la Harpe and G. Skandalis concerning the internal structure of simple -algebras are extended to -algebras that are inductive limits of finite direct sums of homogeneous -algebras. The generalizations are obtained with slightly varying assumptions on the building blocks, but all results are applicable to unital simple inductive limits of finite direct sums of circle algebras.
Finite sums of commutators in -algebras
We prove that for many -algebras, the null space of all finite traces is spanned by finite sums of commutators.
Finite-dimensional Hilbert -modules.
Fonctions de mailles et théorie elliptique des opérateurs aux différences finies (suite)
Formes multilinéaires dans les W*-algèbres.
Fredholm Theories of Mixed Type with Analytic Index Functions.
Functional calculus and spectral theory of locally C*-sums of locally m-convex C*-algebras
Gabor Time-Frequency Lattices and the Wexler-Raz Identity.