We consider the spectrum-preserving maps on positive definite cones of C<sup>*</sup>-algebras or von Neumann algebras. We first introduce some basic properties of Jordan isomorphism. Then, we study the add...We consider the spectrum-preserving maps on positive definite cones of C<sup>*</sup>-algebras or von Neumann algebras. We first introduce some basic properties of Jordan isomorphism. Then, we study the additively spectrum preserving property and the multiplicatively spectrum-preserving property, and prove that these maps can be characterized by Jordan isomorphisms between C<sup>*</sup>-algebras.展开更多
文摘We consider the spectrum-preserving maps on positive definite cones of C<sup>*</sup>-algebras or von Neumann algebras. We first introduce some basic properties of Jordan isomorphism. Then, we study the additively spectrum preserving property and the multiplicatively spectrum-preserving property, and prove that these maps can be characterized by Jordan isomorphisms between C<sup>*</sup>-algebras.