Some remarks on C*-bigebras and duality.
Some remarks on Gleason measures
This work is devoted to generalizing the Lebesgue decomposition and the Radon-Nikodym theorem to Gleason measures. For that purpose we introduce a notion of integral for operators with respect to a Gleason measure. Finally, we give an example showing that the Gleason theorem does not hold in non-separable Hilbert spaces.
Some remarks on measures on orthogonal rational projections and the rational sphere.
Some remarks on quantum and braided group gauge theory
We clarify some aspects of quantum group gauge theory and its recent generalisations (by T. Brzeziński and the author) to braided group gauge theory and coalgebra gauge theory. We outline the diagrammatic version of the braided case. The bosonisation of any braided group provides us a trivial principal bundle in three ways.
Some remarks on the convergence in measure and on a dominated sequence of operators measurable with respect to a semifinite von Neumann algebra
Some results on non-commutative Banach function spaces.
Some Results on the Fourier-Stieltjes Algebra of a Locally Compact Group.
Sommes de commutateurs dans les algèbres de von Neumann finies continues
Soit une algèbre de von Neumann finie. Nous montrons que l’espace des sommes finies de commutateurs de coïncide avec le noyau de la trace centrale. Si est un facteur, il en résulte par exemple que tout élément est une combinaison linéaire finie de projecteurs de dimension . Nous montrons aussi dans ce cas que le groupe dérivé de coïncide avec le noyau du déterminant de Fuglede-Kadison.
Sous-groupes maximaux de groupes classiques associés à certaines C*-algèbres.
Spatiality of derivations of Fréchet GB*-algebras
We show that every continuous derivation of a countably dominated Fréchet GB*-algebra A is spatial whenever A is additionally an AO*-algebra.
Spectra of actions on type I C*-algebras.
Spectral distances: results for Moyal plane and noncommutative torus.
Spectral distribution of the free Jacobi process associated with one projection
Given an orthogonal projection P and a free unitary Brownian motion in a W*-non commutative probability space such that Y and P are *-free in Voiculescu’s sense, we study the spectral distribution νₜ of Jₜ = PYₜPYₜ*P in the compressed space. To this end, we focus on the spectral distribution μₜ of the unitary operator SYₜSYₜ*, S = 2P - 1, whose moments are related to those of Jₜ via a binomial-type expansion already obtained by Demni et al. [Indiana Univ. Math. J. 61 (2012)]. In this connection,...
Spectral dominance and Young's inequality in type III factors.
Spectral Formulas in Quotient C*-Algebras.
Spectral isometries
In this survey, we summarise some of the recent progress on the structure of spectral isometries between C*-algebras.
Spectral Pairs in Cartesian Coordinates.
Spectral subspaces and non-commutative Hilbert transforms
Let G be a locally compact abelian group and ℳ be a semifinite von Neumann algebra with a faithful semifinite normal trace τ. We study Hilbert transforms associated with G-flows on ℳ and closed semigroups Σ of Ĝ satisfying the condition Σ ∪ (-Σ) = Ĝ. We prove that Hilbert transforms on such closed semigroups satisfy a weak-type estimate and can be extended as linear maps from L¹(ℳ,τ) into . As an application, we obtain a Matsaev-type result for p = 1: if x is a quasi-nilpotent compact operator...
Spectral Theory for A (X).
Spectral theory for facially homogenous symmetric self-dual cones.