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...

Dialgebras are a generalization of associative algebras which gives rise to Leibniz algebras instead of Lie algebras. In this paper we deene the dialgebra (co)homology with coeecients, recovering, for constant coeecients, the natural bar homology of dialgebras introduced by J.-L. Loday in L6] and denoted by HY. We show that the homology HY has the main expected properties: it is a derived funct...

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...

Throughout, all rings are associative with an identity element but not necessarily commutative. During the decade of 1980s, a series of papers appeared in the Canadian Journal of Mathematics [1, 2] that had investigated pairs of commutative rings with the same set of prime ideals. In this paper, we consider some generalizations of that study in the noncommutative setting. Consider the ring R= H...

We simplify some conjectures in quantum information theory; the additivity of minimal output entropy, the multiplicativity of maximal output p-norm and the superadditivity of convex closure of output entropy. We construct a unital channel for a given channel so that they share the above additivity properties; we can reduce the conjectures for all channels to those for unital channels.

Let A be a simple separable unital locally approximately subhomogeneous C*algebra (locally ASH algebra). It is shown that A ⊗ Q can be tracially approximated by unital Elliott-Thomsen algebras with trivial K1-group, where Q is the universal UHF algebra. In particular, it follows that A is classifiable by the Elliott invariant if A is Jiang-Su stable.

Abstract. For any finite unital commutative idempotent semigroup S, a unital semilattice, we show how to compute the amenability constant of its semigroup algebra l(S), which is always of the form 4n+1. We then show that these give lower bounds to amenability constants of certain Banach algebras graded over semilattices. Our theory applies to certain natural subalgebras of Fourier-Stieltjes alg...

Let A be a unital amenable A∗-algebra, or a unital commutative hermitian Banach ∗-algebra. We show that if ρ : A → B(H) is a bounded homomorphism, then ρ is completely bounded and ‖ρ‖cb ≤ ‖ρ‖2. Mathematics Subject Classification: 46L07; 46k05