We consider maps on positive definite cones of von Neumann algebras preserving unitarily invariant norms of the spectral geometric means. The main results concern Jordan *-isomorphisms between <em>C</em>*-...We consider maps on positive definite cones of von Neumann algebras preserving unitarily invariant norms of the spectral geometric means. The main results concern Jordan *-isomorphisms between <em>C</em>*-algebras, and show that they are characterized by the preservation of unitarily invariant norms of those operations.展开更多
In this paper, we consider the norms related to spectral geometric means and geometric means. When A and B are positive and invertible, we have ||A<sup>-1</sup>#B|| ≤ ||A<sup>-1</sup>σ<sub...In this paper, we consider the norms related to spectral geometric means and geometric means. When A and B are positive and invertible, we have ||A<sup>-1</sup>#B|| ≤ ||A<sup>-1</sup>σ<sub>s</sub>B||. Let H be a Hilbert space and B(H) be the set of all bounded linear operators on H. Let A ∈ B(H). If ||A#X|| = ||Aσ<sub>s</sub>X||, ?X ∈ B(H)<sup>++</sup>, then A is a scalar. When is a C*-algebra and for any , we have that ||logA#B|| = ||logAσ<sub>s</sub>B||, then is commutative.展开更多
文摘We consider maps on positive definite cones of von Neumann algebras preserving unitarily invariant norms of the spectral geometric means. The main results concern Jordan *-isomorphisms between <em>C</em>*-algebras, and show that they are characterized by the preservation of unitarily invariant norms of those operations.
文摘In this paper, we consider the norms related to spectral geometric means and geometric means. When A and B are positive and invertible, we have ||A<sup>-1</sup>#B|| ≤ ||A<sup>-1</sup>σ<sub>s</sub>B||. Let H be a Hilbert space and B(H) be the set of all bounded linear operators on H. Let A ∈ B(H). If ||A#X|| = ||Aσ<sub>s</sub>X||, ?X ∈ B(H)<sup>++</sup>, then A is a scalar. When is a C*-algebra and for any , we have that ||logA#B|| = ||logAσ<sub>s</sub>B||, then is commutative.
