Approximate unitary equivalence of normaloid type operators

Approximate unitary equivalence and the topology of Ext(A,B)

Let A, B be unital C*-algebras and assume that A is separable and quasidiagonal relative to B. Let φ,ψ : A → B be unital ∗-homomorphisms. If A is nuclear and satisfies the UCT, we prove that φ is approximately stably unitarily equivalent to ψ if and only if φ∗ = ψ∗ : K∗(A,Z/n) → K∗(B,Z/n) for all n ≥ 0. We give a new proof of a result of [DE2] which states that if A is separable and quasidiagon...

Some equivalence classes of operators on B(H)

Robertson-type Theorems for Countable Groups of Unitary Operators

Let G be a countably infinite group of unitary operators on a complex separable Hilbert space H. Let X = {x1, ..., xr} and Y = {y1, ..., ys} be finite subsets of H, r < s, V0 = spanG(X), V1 = spanG(Y ) and V0 ⊂ V1. We prove the following result: Let W0 be a closed linear subspace of V1 such that V0 ⊕ W0 = V1 (i.e., V0 + W0 = V1 and V0 ∩ W0 = {0}). Suppose that G(X) and G(Y ) are Riesz bases for...

The Range of Approximate Unitary Equivalence Classes of Homomorphisms from AH-algebras

Let C be a unital AH-algebra and A be a unital simple C∗-algebra with tracial rank zero. It has been shown that two unital monomorphisms φ, ψ : C → A are approximately unitarily equivalent if and only if [φ] = [ψ] in KL(C,A) and τ ◦ φ = τ ◦ ψ for all τ ∈ T (A), where T (A) is the tracial state space of A. In this paper we prove the following: Given κ ∈ KL(C,A) with κ(K0(C)+\{0}) ⊂ K0(A)+\{0} an...

Generalized Unitary Operators

1. Let C be the complex field and T be the unit circle { \ £ C : | \ | = 1} . For a non-negative integer m or for m = oo, let OCT) be the space of all m-times continuously differentiable functions on T. (Here we consider T as a C°°-manifold in the natural way. Thus, any / £ C m ( r ) can be identified with an m-times continuously differentiable periodic function f (6) of a real variable 0 with ...