On Some Properties of the Norm of the Spectral Geometric Mean  

作　　者：Xiangrui Kong Xiangrui Kong(School of Mathematical Sciences, Qufu Normal University, Qufu, China)

机构地区：[1]School of Mathematical Sciences, Qufu Normal University, Qufu, China

出　　处：《Journal of Applied Mathematics and Physics》2022年第12期3629-3634,共6页应用数学与应用物理（英文）

摘　　要：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^-1#B|| ≤ ||A^-1σ_sB||. 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_sX||, ?X ∈ B(H)⁺⁺, then A is a scalar. When is a C*-algebra and for any , we have that ||logA#B|| = ||logAσ_sB||, then is commutative.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^-1#B|| ≤ ||A^-1σ_sB||. 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_sX||, ?X ∈ B(H)⁺⁺, then A is a scalar. When is a C*-algebra and for any , we have that ||logA#B|| = ||logAσ_sB||, then is commutative.

关 键 词：Kubo-Ando Means Spectral Geometric Mean Geometric Mean C*-Algebra 

分 类 号：O17[理学—数学]