Recent zbMATH articles in MSC 46Mhttps://www.zbmath.org/atom/cc/46M2021-04-16T16:22:00+00:00WerkzeugConvolution type \(C^*\)-algebras.https://www.zbmath.org/1456.460442021-04-16T16:22:00+00:00"Nourouzi, Kourosh"https://www.zbmath.org/authors/?q=ai:nourouzi.kourosh"Reza, Ali"https://www.zbmath.org/authors/?q=ai:reza.aliSummary: In this paper, by using the notion of convolution types we introduce symmetric and non-symmetric convolution type \(C^*\)-algebras. It is shown that any (exact) convolution type induces a (an exact) functor on the category of \(C^*\)-algebras. In particular, any group induces a convolution type and a functor on the category of \(C^*\)-algebras. It is also shown that discrete crossed product of \(C^*\)-algebras and discrete inverse semigroup \(C^*\)-algebras can be considered as convolution type \(C^*\)-algebras.The boundary model for the continuous cohomology of \(\mathrm{Isom}^+ (\mathbb H^n)\).https://www.zbmath.org/1456.220042021-04-16T16:22:00+00:00"Pieters, Hester"https://www.zbmath.org/authors/?q=ai:pieters.hesterSummary: We prove that the continuous cohomology of \(\mathrm{Isom}^+ (\mathbb H^n)\) can be measurably realized on the boundary of hyperbolic space. This implies in particular that for \(\mathrm{Isom}^+ (\mathbb H^n)\) the comparison map from continuous bounded cohomology to continuous cohomology is injective in degree 3. We furthermore prove a stability result for the continuous bounded cohomology of \(\mathrm{Isom}(\mathbb H^n)\) and\(\mathrm{Isom}(\mathbb H^n_\mathbb C)\).On extrapolation properties of Schatten-von Neumann classes.https://www.zbmath.org/1456.470052021-04-16T16:22:00+00:00"Lykov, K. V."https://www.zbmath.org/authors/?q=ai:lykov.konstantin-vSummary: For a certain special class of symmetric sequence spaces, we give an explicit relation between the interpolation and extrapolation representations. This relation is carried over to symmetrically normed ideals of compact operators.Discrete noncommutative Gel'fand Naĭmark duality.https://www.zbmath.org/1456.460612021-04-16T16:22:00+00:00"Bertozzini, Paolo"https://www.zbmath.org/authors/?q=ai:bertozzini.paolo"Conti, Roberto"https://www.zbmath.org/authors/?q=ai:conti.roberto.1"Pitiwan, Natee"https://www.zbmath.org/authors/?q=ai:pitiwan.nateeSummary: We present, in a simplified setting, a non-commutative version of the well-known Gel'fand-Naĭmark duality (between the categories of compact Hausdorff topological spaces and commutative unital \(C^*\)-algebras), where ``geometric spectra'' consist of suitable finite bundles of one-dimensional \(C^*\)-categories equipped with a transition amplitude structure satisfying saturation conditions. Although this discrete duality actually describes the trivial case of finite-dimensional \(C^*\)-algebras, the structures are here developed at a level of generality adequate for the formulation of a general topological/uniform Gel'fand-Naĭmark duality, fully addressed in a companion work.Topological tensor products and quantum entanglement.https://www.zbmath.org/1456.810042021-04-16T16:22:00+00:00"Sokoli, Florian"https://www.zbmath.org/authors/?q=ai:sokoli.florianSummary: This book belongs to one of the most interesting and promising phenomena in today's quantum information sciences. Although being known for several decades, its intriguing features are still insufficiently understood. This work is intended to tackle this problem using the mathematical tool of topological tensor products. With this approach several important results on quantum entanglement of distinguishable and indistinguishable particles are proven including sophisticated aspects related to Schmidt numbers, Slater numbers and genuine multipartite entanglement. The work is supplemented by an introduction to the mathematical background of topological tensor products, which may serve as an extensive reference in its on right.