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Molnár, L. (2017) The Arithmetic, Geometric and Harmonic Means in Operator Algebras and Transformations among Them. In: Botelho, F., King, R. and Rao, T.S.S.R.K., Eds., Recent Methods and Research Advances in Operator Theory, Contemporary Mathematics, Vol. 687, The American Mathematical Society, Providence, 182-193.

has been cited by the following article:

• 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.