In the group of (continuous) Jordan automorphisms, with the uniform topology, on a semisimple Banach algebra, we show that the connected component of the identity consists of automorphisms. P. Civin and B. Yood have shown that a Jordan homomorphism (that is, a homomorphism that preserves the product xoy = | (xy+yx)) from a Banach algebra onto a semisimple Banach algebra is continuous provided t...

Let A be an algebra over a commutative unital ring C. We say that A is zero triple product determined if for every C-module X and every trilinear map {·, ·, ·}, the following holds: if {x, y, z} 0 whenever xyz 0, then there exists a C-linear operator T : A3 −→ X such that {x, y, z} T xyz for all x, y, z ∈ A. If the ordinary triple product in the aforementioned definition is replaced by Jordan t...

We formulate a lattice theoretical Jordan normal form theorem for certain nilpotent lattice maps satisfying the so called JNB conditions. As an application of the general results, we obtain a transparent Jordan normal base of a nilpotent endomorphism in a finitely generated semisimple module.

In this article, it is proved that under some conditions every bijective Jordan triple product homomorphism from generalized matrix algebras onto rings is additive. As a corollary, we obtain that every bijective Jordan triple product homomorphism from Mn(A) (A is not necessarily a prime algebra) onto an arbitrary ring R is additive.

David maps are generalizations of classical planar quasiconformal maps for which the dilatation is allowed to tend to infinity in a controlled fashion. In this note we examine how these maps distort Hausdorff dimension. We show: – Given α and β in [0, 2] , there exists a David map φ: C → C and a compact set Λ such that dimH Λ = α and dimH φ(Λ) = β . – There exists a David map φ: C → C such that...

In this note, we will discuss what kind of operators between C*-algebras preserves Jordan triple products {a, b, c} = (abc + cba)/2. These include especially isometries and disjointness preserving operators.

In this paper we review the definition of the monodromy of an angle valued map based on linear relations as proposed in [3]. This definition provides an alternative treatment of the Jordan cells, topological persistence invariants of a circle valued maps introduced in [2]. We give a new proof that homotopic angle valued maps have the same monodromy, hence the same Jordan cells, and we show that...

In this paper, we characterize rank one preserving module maps on a Hilbert C∗−module and study its applications on free probability theory.

Let G ⊂ GL(V ) be a complex reductive group. Let G denote {φ ∈ GL(V ) | p◦φ = p for all p ∈ C[V ]}. We show that, in general, G = G. In case G is the adjoint group of a simple Lie algebra g, we show that G is an order 2 extension of G. We also calculate G for all representations of SL2.