K-theory has helped convert the theory of operator algebras from a simple branch of
functional analysis to a subject with broad applicability throughout mathematics, especially …

This volume attempts to give a comprehensive discussion of the theory of operator algebras
(C*-algebras and von Neumann algebras.) The volume is intended to serve two purposes: to …

For any irrational number α let A α be the transformation group C∗-algebra for the action of
the integers on the circle by powers of the rotation by angle 2 πα. It is known that A α is …

The possibility that nuclear (or amenable) C*-algebras should be classified up to
isomorphism by their K-theory and related invariants was raised in an article by Elliott …

Suppose that A is a C*-algebra for which, where is the Jiang–Su algebra: a unital, simple,
stably finite, separable, nuclear, infinite-dimensional C*-algebra with the same Elliott …

We show in Section 3 that all simple dimension groups with finitely many pure states (see
Section 1) arise in this fashion. A generalization of this result to all simple dimension groups …

Let D be a simple unital C∗-algebra, let B be a UHF-algebra, and put A= B⊗ D. It is proved
that if p, q ϵ A are projections and τ (p)< τ (q) for all quasitraces τ on A, then p≲ q (in the …

In order to make available for C*-atgebras the results of Goodearl and Handelman [5] on
existence and uniqueness of rank functions on regular rings, we associate in the present …

Page 1 PURE AND APPLIED MATHEMATICS A Series of Monographs and Textbooks LINEAR
ALGEBRA OVER COMMUTATIVE RINGS Bernard R. McDonald Page 2 Linear Algebra Over …

We introduce an equivalence relation among the positive elements in a C∗ and show that
the algebra is (semi-) finite if and only if there is a separating family of (semi-) finite traces …