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.
