Let A be a simple separable unital C*-algebra satisfying the UCT, and assume that A has finite decomposition rank. Let Q denote the UHF algebra with K0(Q) = Q. Then A⊗Q can be tracially approximated by unital Elliott-Thomsen algebras, and therefore A ⊗ Z is an ASH algebra (hence classifiable), where Z is the Jiang-Su algebra.

Starting from Kirchberg’s theorems announced at the operator algebra conference in Genève in 1994, namely O2 ⊗A ∼= O2 for separable unital nuclear simple A and O∞ ⊗A ∼= A for separable unital nuclear purely infinite simple A, we prove that KK-equivalence implies isomorphism for nonunital separable nuclear purely infinite simple C∗-algebras. It follows that if A and B are unital separable nuclea...

Let X be a compact metric space and let α be a homeomorphism on X. Related to a theorem of Pimsner, we show that C(X) ⋊α Z can be embedded into a unital simple AF-algebra if and only if there is a strictly positive α-invariant Borel probability measure. Suppose that Λ is a Z action on X. If C(X)⋊Λ Z can be embedded into a unital simple AF-algebra, then there must exist a strictly positive Λ-inv...

The notation and terminology used in this paper have been introduced in the following articles: [3], [19], [9], [10], [16], [20], [4], [5], [22], [23], [21], [1], [6], [17], [18], [2], [25], [26], [24], [15], [12], [13], [8], [14], and [7]. Let A be a non empty set, x be an element, and a be an element of A. Let us observe that (A 7−→ x)(a) reduces to x. Let A, B be non empty topological spaces...

We introduce a new concept of the bounded rank (with respect to a positive constant) for unital C∗-algebras as a modification of the usual real rank. We present a series of conditions insuring that bounded and real ranks coincide. These observations are then used to prove that for a given n and K > 0 there exists a separable unital C∗-algebra Z n such that every other separable unital C∗-algebr...

Let G be the group of projectivities stabilizing a unital U in PG(2, q2). In this paper, we prove that U is a classical unital if and only if there are two points in U such that the stabilizer of these two points in G has order q2 − 1.

For two algebras $A$ and $B$, a linear map $T:A longrightarrow B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for all $x,yin A$. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear se...