TITLE:
On Some Properties of the Norm of the Spectral Geometric Mean
AUTHORS:
Xiangrui Kong
KEYWORDS:
Kubo-Ando Means, Spectral Geometric Mean, Geometric Mean, C*-Algebra
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.12,
December
21,
2022
ABSTRACT: 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-1σsB||. 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|| = ||AσsX||, ?X ∈ B(H)++, then A is a scalar. When is a C*-algebra and for any , we have that ||logA#B|| = ||logAσsB||, then is commutative.