Additive maps on standard operator algebras preserving parts of the spectrum

A Note on Spectrum Preserving Additive Maps on C*-Algebras

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.

Multiplicative bijective maps on standard operator algebras

Spectrum Preserving Linear Maps Between Banach Algebras

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.

multiplicative bijective maps on standard operator algebras

Jordan Maps on Standard Operator Algebras

Jordan isomorphisms of rings are defined by two equations. The first one is the equation of additivity while the second one concerns multiplicativity with respect to the so-called Jordan product. In this paper we present results showing that on standard operator algebras over spaces with dimension at least 2, the bijective solutions of that second equation are automatically additive.