In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.

3. You are already familiar with the concept of vector spaces in the form of …nite dimensional Euclidean vector spaces, and most of what we do in these lectures will involve these spaces (and, indeed, will also assume that the dot product operation is well-de…ned so that we can de…ne the matrix operations associated with linear transformations). However, it will also be useful to consider some ...

We observe a disconnect between the developers and end users of linear algebra libraries. On one hand, numerical high-performance communities invest significant effort in development optimization highly sophisticated kernels libraries, aiming at maximum exploitation both properties input matrices, architectural features target computing platform. other are progressively less likely to go throug...

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 ...