Index structures are one of the most important tools that DBAs leverage in order to improve the performance of analytics and transactional workloads. However, with the explosion of data that is constantly being generated in a wide variety of domains including autonomous vehicles, Internet of Œings (IoT) devices, and E-commerce sites, building several indexes can o‰en become prohibitive and cons...

Almost forty years ago, Connes, Feldman and Weiss proved that for measurable equivalence relations the notions of amenability hyperfiniteness coincide. In this paper we define uniform version graphed bounded vertex degrees prove these two coincide as well. Roughly speaking, a measured graph $\mathcal {G}$ is uniformly hyperfinite if any ${\varepsilon }>0$ there exists $K\geq 1$ such not only {G...

Let (1→Nm→Gm→Qm→1)m∈N be a sequence of extensions finite groups such that their coarse disjoint unions have bounded geometry. In this paper, we show if the (Nm)m∈N and (Qm)m∈N are coarsely embeddable into Hilbert space, then Baum–Connes conjecture holds for union (Gm)m∈N. As an application, relative expanders constructed by G. Arzhantseva R. Tessera, special box spaces free discovered T. Delabi...

We continue the investigation of notions of approximate amenability that were introduced in work of the second and third authors together with R. J. Loy. It is shown that every boundedly approximately contractible Banach algebra has a bounded approximate identity, and that the Fourier algebra of the free group on two generators is not operator approximately amenable. Further examples are obtain...

A kind of Dirac-Connes operator defined in the framework of Connes’ NCG is introduced on discrete abelian groups; it satisfies a Junk-free condition, and bridges the NCG composed by Dimakis, MüllerHoissen and Sitarz and the NCG of Connes. Then we apply this operator to d-dimensional lattices. [email protected] [email protected]

Abstract In this paper, we give a new geometric condition in terms of measured asymptotic expanders to ensure rigidity Roe algebras. Consequently, obtain the for all bounded geometry spaces that coarsely embed into some $L^p$-space $p\in [1,\infty )$. Moreover, also verify box constructed by Arzhantseva–Tessera and Delabie–Khukhro even though they do not any $L^p$-space. The key step our proof ...

Ocneanu noted that the data for what is now known as a Turaev-Viro type TQFT is supplied by a subfactor N of nite index and depth of a II1 factor M . One takes all the irreducible bimodules arising in the decomposition of the tensor powers, in the sense of Connes ([3]), of the Hilbert space L(M) viewed as an N−N bimodule, or, in Connes' terminology, a correspondence. (We will use the term corre...

a definition of two jointly asymptotically nonexpansive mappings s and t on uniformly convex banach space e is studied to approximate common fixed points of two such mappings through weak and strong convergence of an ishikawa type iteration scheme generated by s and t on a bounded closed and convex subset of e. as a consequence of the notion of two jointly asymptotically nonexpansive maps, we c...