Let θ : A → B be a zero-product preserving bounded linear map between C*-algebras. Here neither A nor B is necessarily unital. In this note, we investigate when θ gives rise to a Jordan homomorphism. In particular, we show that A and B are isomorphic as Jordan algebras if θ is bijective and sends zero products of self-adjoint elements to zero products. They are isomorphic as C*-algebras if θ is...

We describe a murine cDNA, designated Early T lymphocyte activation 1 (ETA-1) which is abundantly expressed after activation of T cells. Eta-1 encodes a highly acidic secreted product having structural features of proteins that bind to cellular adhesion receptors. The Eta-1 gene maps to a locus on murine chromosome 5 termed Ric that confers resistance to infection by Rickettsia tsutsugamushi (R...

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.

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...

Norm preserver maps of Jordan product on the algebra Mn of n×n complex matrices are studied, with respect to various norms. A description of such surjective maps with respect to the Frobenius norm is obtained: Up to a suitable scaling and unitary similarity, they are given by one of the four standard maps (identity, transposition, complex conjugation, and conjugate transposition) on Mn, except ...

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.