Abstract We construct two types of unital separable simple $C^*$ -algebras: $A_z^{C_1}$ and $A_z^{C_2}$ , one exact but not amenable, the other nonexact. Both have same Elliott invariant as Jiang–Su algebra – namely, $A_z^{C_i}$ has a unique tracial state, $$ \begin{align*} \left(K_0\left(A_z^{C_i}\right), K_0\left(A_z^{C_i}\right)_+, \left[1_{A_z^{C_i}} \right]\right)=(\mathbb{Z}, \mathbb{Z}_+...

Let Z denote the simple limit of prime dimension drop algebras that has a unique tracial state (cf. Jiang and Su [11]). Let A 6= 0 be a unital C∗-algebra with A ∼= A ⊗ Z. Then the homotopy groups of the group U(A) of unitaries in A are stable invariants, namely, πi(U(A)) ∼= Ki−1(A) for all integer i ≥ 0. Furthermore, A has cancellation for full projections, and satisfies the comparability quest...

Given a self adjoint operator A on a Hilbert space, suppose that that one wishes to compute the spectrum of A numerically. In practice, these problems often arise in such a way that the matrix of A relative to a natural basis is “sparse”. For example, discretized second order differential operators can be represented by doubly infinite tridiagonal matrices. In these cases it is easy and natural...

We prove the free analogue of the transportation cost inequality for tracial distributions of non-commutative self-adjoint (also unitary) multi-variables based on random matrix approximation procedure.

Introduction 1 0.1. Associated primes 2 0.2. Depth 2 1. Regular local rings and their cohomological properties 4 1.1. Notions of dimension 4 1.2. Dualizing functor 5 1.3. Local rings 6 1.4. Serre’s theorem on regular local rings 6 1.5. Cohomology of D when global dimension is finite 8 2. Depth 8 2.1. Property (Sk) 8 2.2. Serre’s criterion of normality 10 2.3. Cohen-Macaulay modules 11 3. Diviso...

In process algebras like μCRL and ACP communication is defined globally. In the context of component-based architectures one wishes to define subcomponents of a system separately, including communication within that subcomponent. We define a process algebra with an operator for local communication that facilitates component-based architectures. Besides being compositional, this language is aime...

For a lattice system with a finite number of Fermions and spins on each lattice point, conditional expectations relative to an even product state (such as Fermion Fock vacuum) are introduced and the corresponding standard potential for any given dynamics, or more generally for any given time derivative (at time 0) of strictly local operators, is defined, with the case of the tracial state previ...

Abstract Let $$\phi $$ ϕ be a positive map from the $$n\times n$$ n × matrices $$\mathcal {M}_n$$ M to $$m\times m$$ m {M}_m$$ . It is known that 2-positive if and only for all $$K\in \mathcal <mm...