Equivariant KK-theory and the Novikov conjecture.
Equivariant local cyclic homology and the equivariant Chern-Connes character.
Equivariant measurable liftings
We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Möbius group of the projective line. Since the general proof is very simple but not explicit, we also provide a much more explicit lifting for semisimple Lie groups acting on their Furstenberg boundary, using unrestricted Fatou convergence. This setting is relevant to -cocycles for characteristic classes.
Equivariant Morita equivalences between Podleś spheres
We show that the family of Podleś spheres is complete under equivariant Morita equivalence (with respect to the action of quantum SU(2)), and determine the associated orbits. We also give explicit formulas for the actions which are equivariantly Morita equivalent with the quantum projective plane. In both cases, the computations are made by examining the localized spectral decomposition of a generalized Casimir element.
Equivariant sheaf cohomology.
Equivariant spectral triples
We present the review of noncommutative symmetries applied to Connes' formulation of spectral triples. We introduce the notion of equivariant spectral triples with Hopf algebras as isometries of noncommutative manifolds, relate it to other elements of theory (equivariant K-theory, homology, equivariant differential algebras) and provide several examples of spectral triples with their isometries: isospectral (twisted) deformations (including noncommutative torus) and finite spectral triples.
Ergodic Actions by Compact Groups on C*-Algebras.
Ergodic actions of compact groups on operator algebras. III. Classification for SU (2).
Ergodic Dilation of a Quantum Dynamical System
Using the Nagy dilation of linear contractions on Hilbert space and the Stinespring’s theorem for completely positive maps, we prove that any quantum dynamical system admits a dilation in the sense of Muhly and Solel which satisfies the same ergodic properties of the original quantum dynamical system.
Ergodic power functions for mean bounded, invertible, positive operators
Ergodic properties and KMS conditions on -symbolic dynamical systems.
Ergodic results for certain contractions on Orlicz spaces with fixed points.
Ergodic Theorem for Convex Sets and Operator Algebras.
Ergodic theorems for certain power bounded operators.
Ergodic theorems for contractions in Orlicz-Kantorovich lattices.
Ergodic Theorems for Noncommutative Dynamical Systems.
Ergodic theorems in fully symmetric spaces of τ-measurable operators
Junge and Xu (2007), employing the technique of noncommutative interpolation, established a maximal ergodic theorem in noncommutative -spaces, 1 < p < ∞, and derived corresponding maximal ergodic inequalities and individual ergodic theorems. In this article, we derive maximal ergodic inequalities in noncommutative -spaces directly from the results of Yeadon (1977) and apply them to prove corresponding individual and Besicovitch weighted ergodic theorems. Then we extend these results to noncommutative...
Ergodic theorems in -lattice cones
Errata
Errata