Related papers: Homomorphisms from AH-algebras

We show that, if $f$ is an outer function and $a\in[0,1)$, then the set of functions $\{\log |(f\circ\psi)^*|: \psi:\mathcal{D}\to\mathcal{D} \text{ holomorphic}, |\psi(0)|\le a\}$ is uniformly integrable on the unit circle. As an…

Let $X$ be a locally compact Hausdorff space, let $A$ be a partially ordered algebra, and let $\pi\colon \mathrm{C}_{\mathrm c}(X)\to A$ be a positive algebra homomorphism. Under conditions on $A$ that are satisfied in a good number of…

We prove that if two nonzero homomorphisms from the Cuntz algebra O_infinity to a purely infinite simple C*-algebra have the same class in KK-theory, and if either both are unital or both are nonunital, then they are approximately unitarily…

We prove that the pure state space is homogeneous under the action of the automorphism group (or a certain smaller group of approximately inner automorphisms) for a fairly large class of simple separable nuclear C*-algebras, including the…

We study the limits of inductive sequences (A_i,\phi_i) where each A_i is a direct sum of full matrix algebras over compact metric spaces and each partial map of \phi_i is diagonal. We give a new characterisation of simplicity for such…

Let $\mathcal{A}$ and $\mathcal{B}$ be two unital $C^*$-algebras and let for $C\in\mathcal{A},\ \Gamma_C=\{\gamma \in \mathbb{C} : \|C-\gamma I\|=\inf_{\alpha\in \mathbb{C}} \|C-\alpha I\|\}$. We prove that if $\Phi :\mathcal{A}…

We establish axiomatic characterizations of $K$-theory and $KK$-theory for real C*-algebras. In particular, let $F$ be an abelian group-valued functor on separable real C*-algebras. We prove that if $F$ is homotopy invariant, stable, and…

Suppose A and B are unital C*-algebras and A is separable. Let Rep(A,B) denote the set of all unital *-homomorphisms from A to B with the topology of pointwise convergence. We consider the problem of when the closure of the unitary orbit of…

Starting from Kirchberg's theorems announced in 1994, namely O_2 tensor A is isomorphic to O_2 for separable unital nuclear simple A and O_infinity tensor A is isomorphic to A if in addition A is purely infinite, we prove that…

Let $A(G)$ and $B(H)$ be the Fourier and Fourier-Stieltjes algebras of locally compact groups $G$ and $H$, respectively. Ilie and Spronk have shown that continuous piecewise affine maps $\alpha: Y \subseteq H\rightarrow G$ induce completely…

We study the automorphism group of a unital, simple, $\mathcal{Z}$-stable $C^{*}$-algebra. In this paper, we generalize the results by the authors in \cite{pr_auto} to $\mathcal{Z}$-stable $C^{*}$-algebras $\mathfrak{A}$ such that…

We show that any compact quantum group having the same fusion rules as the ones of $SO(3)$ is the quantum automorphism group of a pair $(A, \varphi)$, where $A$ is a finite dimensional $C^*$-algebra endowed with a homogeneous faithful…

Let $A$ be a unital simple separable exact C$^*$-algebra which is approximately divisible and of real rank zero. We prove that the set of positive elements in $A$ with a fixed Cuntz class is path connected. This result applies in particular…

We study the composition operators $C_a$ acting on the Hardy space $H^2$ of the unit disk, given by $C_af=f\circ\varphi_a$, where $$ \varphi_a(z)=\frac{a-z}{1-\bar{a}z}, $$ for $|a|<1$. These operators are reflections: $C_a^2=1$. We study…

We show that, if a simple $C^{*}$-algebra $A$ is topologically finite-dimensional in a suitable sense, then not only $K_{0}(A)$ has certain good properties, but $A$ is even accessible to Elliott's classification program. More precisely, we…

Let $A$ be a unital separable simple infinite dimensional \CA with tracial rank no more than one and with the tracial state space $T(A)$ and let $U(A)$ be the unitary group of $A.$ Suppose that $u\in U_0(A),$ the connected component of…

A reduction $\varphi$ of an ordered group $(G,P)$ to another ordered group is an order homomorphism which maps each interval $[1,p]$ bijectively onto $[1, \varphi(p)]$. We show that if $(G,P)$ is weakly quasi-lattice ordered and reduces to…

A mapping $f:(G_1,[ ]_1)\to (G_2,[ ]_2)$ between ternary semigroups will be called a ternary homomorphism if $f([xyz]_1)=[f(x)f(y)f(z)]_2$. In this paper, we prove the generalized Hyers--Ulam--Rassias stability of mappings of commutative…

Two sesquilinear forms $\Phi:\mathbb C^m\times\mathbb C^m\to \mathbb C$ and $\Psi:\mathbb C^n\times\mathbb C^n\to \mathbb C$ are called topologically equivalent if there exists a homeomorphism $\varphi :\mathbb C^m\to \mathbb C^n$ (i.e., a…

Let $G$ be an inductive limit of finite cyclic groups and let $A$ be a unital simple projectionless C*-algebra with $K_1(A) \cong G$ and with a unique tracial state, as constructed based on dimension drop algebras by Jiang and Su. First, we…