Remarks on Essential Codimension
We look for generalizations of the Brown-Douglas-Fillmore essential codimension result, leading to interesting local uniqueness theorems in $KK$-theory. We also study the structure of Paschke dual algebras.
math.OA↗
arXiv subjects
Ping W. Ng
Publications and source records attributed to Ping W. Ng.
A relative bicommutant theorem: the stable case of Pedersen's question
In 1976, D. Voiculescu proved that every separable unital sub-C*-algebra of the Calkin algebra is equal to its (relative) bicommutant. In his minicourse (see reference), G. Pedersen asked in 1988 if Voiculescu's theorem can be extended to a simple corona algebra of a $σ$-unital C*-algebra. In this note, we answer Pedersen's question for a stable $σ$-unital C*-algebra.
math.OA↗
Commutators and linear spans of projections in certain finite C*-algebras
Assume that A is a unital separable simple C*-algebra with real rank zero, stable rank one, strict comparison of projections, and that its tracial simplex T(A) has a finite number of extremal points. We prove that every self-adjoint element a in A in the kernel of all tracial states is the sum of two commutators in A and that every positive element of A is a linear combination of projections with positive coefficients. Assume that A is as above but σ-unital. Then an element (resp. a positive element) a of A is a linear combination (resp. a linear combination with positive coefficients) of projections if and only if for all τin T(A), the extension \barτto the enveloping von Neumann algebra has a finite value for the range projection of a. Assume that A is unital and as above but T(A) has infinitely many extremal points. Then A is not the linear span of its projections. This result settles two open problems of Marcoux.
math.OA↗
Some consequences of von Neumann algebra uniqueness
In this note, we derive some consequences of the von Neumann algebra uniqueness theorems developed in a previous paper (see arXiv:1207.6741v1). In particular, 1) we solvein a paper of Futamura, Kataoka, and Kishimoto, by proving that if A is a separable simple nuclear C*-algebra and for π_1 and π_2 are type III representations of A on a separable Hilbert space, then for π_1 and π_2 being algebraically equivalent, it is necessary and sufficient that there is an automorphism αof A such that π_1 composed with α, and π_2 are quasi-equivalent. 2) we give a new (short) proof of the equivalence of injectivity and extreme amenability (of the corresponding unitary group) for countably decomposable properly infinite von Neumann algebras. 3) using ideas of Pestov, we show that the Connes embedding problem is equivalent to many topological groups having the Kirchberg property.
math.OA↗