On the $KK$-theory of strongly self-absorbing $C^{*}$-algebrasMathematica Scandinavica - Tập 104 Số 1 - Trang 95
Marius Dădărlat, Wilhelm Winter
Let $\mathcal D$ and $A$ be unital and separable $C^{*}$-algebras; let $\mathcal D$ be strongly self-absorbing. It is known that any two unital ${}^*$-homomorphisms from $\mathcal D$ to $A \otimes \mathcal D$ are approximately unitarily equivalent. We show that, if $\mathcal D$ is also $K_{1}$-injective, they are even asymptotically unitarily equivalent. This in particular implies that any...... hiện toàn bộ
Periodic points of equivariant mapsMathematica Scandinavica - Tập 107 Số 2 - Trang 224
Jerzy Jezierski, Wacław Marzantowicz
We assume that $X$ is a compact connected polyhedron, $G$ is a finite group acting freely on $X$, and $f:X\to X$ a $G$-equivariant map. We find formulae for the least number of $n$-periodic points in the equivariant homotopy class of $f$, i.e., $\inf_h |(\mathrm{Fix}(h^n)|$ (where $h$ is $G$-homotopic to $f$). As an application we prove that the set of periodic points of an equivariant map...... hiện toàn bộ
Locally compact quantum groups in the von Neumann algebraic settingMathematica Scandinavica - Tập 92 Số 1 - Trang 68
Johan Kustermans, Stefaan Vaes
In this paper we complete in several aspects the picture of locally compact quantum groups. First of all we give a definition of a locally compact quantum group in the von Neumann algebraic setting and show how to deduce from it a $C^*$-algebraic quantum group. Further we prove several results about locally compact quantum groups which are important for applications, but were not yet settl...... hiện toàn bộ