Related papers: Quasi-local Algebras and Asymptotic Expanders

A C*-algebra is determined to a great extent by the partial order of its commutative C*-algebras. We study order-theoretic properties of this dcpo. Many properties coincide: the dcpo is, equivalently, algebraic, continuous, meet-continuous,…

For elements $a, b$ of a C*-algebra we denote $a=ab$ by $a\ll b$. We show that all $\omega_1$-unital C*-algebras have $\ll$-increasing approximate units, extending a classical result for $\sigma$-unital C*-algebras. We also construct (in…

The purpose of this note is to characterize the asymptotic dimension $asdim(X)$ of metric spaces $X$ in terms similar to Property A of Yu: If $(X,d)$ is a metric space and $n\ge 0$, then the following conditions are equivalent: [a.]…

Consider the semialgebraic structure over the real field. More generally, let an ominimal structure be over a real closed field. We show that a definable metric space X with a definable metric d is embedded into a Euclidean space so that…

We introduce notions of the Rohlin property and the approximate representability for inclusions of unital $C^*$-algebras. We investigate a dual relation between the Rohlin property and the approximate representability. We prove that a…

This paper is a revision and an enlargement of the previous version titled "Extreme points of the unit ball of a quasi-multiplier space" which had been circulated since 2004. We study extreme points of the unit ball of an operator space by…

In this paper we study structural and uniqueness questions for Cartan subalgebras of uniform Roe algebras. We characterise when an inclusion $B\subseteq A$ of $\mathrm{C}^*$-algebras is isomorphic to the canonical inclusion of…

We formulate a mathematical setup for computational neural networks using noncommutative algebras and near-rings, in motivation of quantum automata. We study the moduli space of the corresponding framed quiver representations, and find…

We introduce a compactification construction for abstract quasi-local C*-algebras over countable metric spaces equipped with an isometric group action which is functorial with respect to bounded spread isomorphisms. In $1$D, the…

We use the general notion of set of indices to construct algebras of nonlinear generalized functions of Colombeau type. They are formally defined in the same way as the special Colombeau algebra, but based on more general growth condition…

A general notion of a quasi-finite algebra is introduced as an algebra graded by the set of all integers equipped with topologies on the homogeneous subspaces satisfying certain properties. An analogue of the regular bimodule is introduced…

The convex closure of entropy vectors for quasi-uniform random vectors is the same as the closure of the entropy region. Thus, quasi-uniform random vectors constitute an important class of random vectors for characterizing the entropy…

We explore the geometry and asymptotics of extended Racah coeffecients. The extension is shown to have a simple relationship to the Racah coefficients for the positive discrete unitary representation series of SU(1,1) which is explicitly…

We investigate the rigidity of the $\ell^p$ analog of Roe-type algebras. In particular, we show that if $p\in[1,\infty)\setminus\{2\}$, then an isometric isomorphism between the $\ell^p$ uniform Roe algebras of two metric spaces with…

Conic quasi-linear maps are nonlinear operators from $C_0(X)$ to a normed linear space $E$ which preserve nonnegative linear combinations on positive cones generated by single functions; quasi-linear maps are linear on singly generated…

Two extension problems are solved. First, the class of locally matricial algebras over an arbitrary field is closed under extensions. Second, the class of locally finite dimensional semisimple algebras over a fixed field is closed under…

In this paper we present a systematic study of regular sequences of quasi-nonexpansive operators in Hilbert space. We are interested, in particular, in weakly, boundedly and linearly regular sequences of operators. We show that the type of…

It has been discussed earlier that ( weak quasi-) quantum groups allow for conventional interpretation as internal symmetries in local quantum theory. From general arguments and explicit examples their consistency with (braid-) statistics…

We study the geometry of warped cones over free, minimal isometric group actions and related constructions of expander graphs. We prove a rigidity theorem for the coarse geometry of such warped cones: Namely, if a group has no abelian…

The aim of this paper is to investigate properties preserved and co-preserved by coarsely $n$-to-1 functions, in particular by the quotient maps $X\to X/\sim$ induced by a finite group $G$ acting by isometries on a metric space $X$. The…