We develop a matricial version of Rieffel’s Gromov-Hausdorff distance for compact quantum metric spaces within the setting of operator systems and unital C∗-algebras. Our approach yields a metric space of “isometric” unital complete order isomorphism classes of metrized operator systems which in many cases exhibits the same convergence properties as those in the quantum metric setting, as for e...

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

For von Neumann algebras M,N not isomorphic to C C and without type I2 summands, we show that for an order-isomorphism f : AbSub M! AbSub N between the posets of abelian von Neumann subalgebras of M and N , there is a unique Jordan ⇤-isomorphism g : M! N with the image g[S] equal to f(S) for each abelian von Neumann subalgebra S of M. The converse also holds. This shows the Jordan structure of ...

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

We construct a functor from the category of elliptic curves to noncommutative tori. Our proof is based on an isomorphism between Sklyanin algebras and dense sub-algebras

Let X, Y be compact, connected, metrisable spaces with base points Xo, Yo and let denote the compact operators. It is shown that Co(X\xo)| is asymptotically homotopic (or shape equivalent) to Co(Y~yo) @ Yi r if and only if X and Y have isomorphic K-groups. Similar results are obtained for certain inductive limits of nuclear C*-algebras. Let ~r denote the category whose objects are all the separ...

In this note, unless we say otherwise every vector space or algebra we speak about is over C. If A is a Banach algebra and e ∈ A satisfies xe = x and ex = x for all x ∈ A, and also ‖e‖ = 1, we say that e is unity and that A is unital. If A is a unital Banach algebra and x ∈ A, the spectrum of x is the set σ(x) of those λ ∈ C for which λe−x is not invertible. It is a fact that if A is a unital B...

Mathieu and Ruddy proved that if be a unital spectral isometry from a unital C*-algebra Aonto a unital type I C*-algebra B whose primitive ideal space is Hausdorff and totallydisconnected, then is Jordan isomorphism. The aim of this note is to show that if be asurjective spectrum preserving additive map, then is a Jordan isomorphism without the extraassumption totally disconnected.