The Kadison-Kastler problem asks whether close C*-algebras on a Hilbert space must be spatially isomorphic. We establish this when one of the algebras is separable and nuclear. We also apply our methods to the study of near inclusions of C*-algebras.

Several isomorphism classes of graph coverings of a graph G have been enumerated by many authors. Kwak and Lee (Canad. J. Math. XLII (1990) 747) enumerated the isomorphism classes of graph bundles and those of n-fold coverings with respect to a group of automorphisms of the base graph G which 9x a spanning tree. Hofmeister (Discrete Math. 98 (1991) 175) independently enumerated the isomorphism ...

We work out the theory of fractional isomorphism graphons as a generalization to classical finite graphs. The is given in terms homomorphism densities trees and it characterized distributions on iterated degree measures, Markov operators, weak conditional expectation with respect invariant sub-σ-algebras certain quotients graphons.

We give a complete invariant for finite-dimensional Hopf C*-algebras. Algebras that are equal under the invariant are the same up to a Hopf *-(co-anti)isomorphism. Résumé. On donne un invariant complet pour les C*-algèbres de Hopf

Assume A is a Fréchet algebra equipped with a smooth isometric action of a vector group V , and consider Rieffel’s deformation AJ of A. We construct an explicit isomorphism between the smooth crossed products V n AJ and V n A. When combined with the Elliott-Natsume-Nest isomorphism, this immediately implies that the periodic cyclic cohomology is invariant under deformation. Specializing to the ...

Let C be a class of graphs closed under isomorphism and let ~ C be obtained from C by arc anchorage. A concept of ~ C-homogeneous graphs that include the C-ultrahomogeneous graphs is given, with the explicit construction of ~ C-homogeneous graphs that are not C-ultrahomogeneous, via ordered pencils of binary projective spaces.