Allen’s well-known Interval Algebra has been developed for temporal representation and reasoning, but there are also interesting spatial applications where intervals can be used. A prototypical example are traffic scenarios where cars and their regions of influence can be represented as intervals on a road as the underlying line. There are several differences of temporal and spatial intervals w...

In this paper, we extend the notion of generalized tracial approximation to non-unital case. An example approximation, which comes from dynamical systems, is also provided. We use machinery Cuntz subequivalence work in setting.

Let A be a unital simple direct limit of recursive subhomogeneous algebras with no dimension growth. We give criteria which specify exactly when A has real rank zero, and exactly when A has the Property (SP): every nonzero hereditary subalgebra of A contains a nonzero projection. Specifically, A has real rank zero if and only if the image of K0(A) in Aff(T (A)) is dense, and A has the Property ...

ABSTRACT. The subject of this paper are polynomials in multiple non-commuting variables. For polynomials of this type orthogonal with respect to a state, we prove a Favardtype recursion relation. On the other hand, free Sheffer polynomials are a polynomial family in non-commuting variables with a resolvent-type generating function. Among such families, we describe the ones that are orthogonal. ...

We prove that every 2-local derivation from the algebra Mn(A)(n > 2) into its bimodule Mn(M) is a derivation, where A is a unital Banach algebra and M is a unital A-bimodule such that each Jordan derivation from A into M is an inner derivation, and that every 2-local derivation on a C*-algebra with a faithful traceable representation is a derivation. We also characterize local and 2-local Lie d...

In this paper, a new construction of vertex algebras from more general vertex operators is given and a notion of quasi module for vertex algebras is introduced and studied. More specifically, a notion of quasi local subset(space) of Hom (W,W ((x))) for any vector space W is introduced and studied, generalizing the notion of usual locality in the most possible way, and it is proved that on any m...

The Connes embedding problem (CEP) is a in the theory of tracial von Neumann algebras and asks whether or not every algebra embeds into an ultrapower hyperfinite II 1 <mml:annotation encoding="application/x-...