Operator Spectral Geometric Versus Geometric Mean

Hamid Reza Moradi; Shigeru Furuichi; Mohammad Sababheh

Operator Spectral Geometric Versus Geometric Mean

Functional Analysis 2023-06-21 v4

Authors: Hamid Reza Moradi , Shigeru Furuichi , Mohammad Sababheh

Abstract

The main goal of this article is to present new inequalities for the spectral geometric mean $A\natural_t B$ of two positive definite operators $A, B$ on a Hilbert space. The obtained results complement many known inequalities for the geometric mean $A\sharp_t B$ . In particular, explicit comparisons between $A\natural_t B$ and $A\sharp_t B$ are given, with applications towards Ando-type inequalities and Ando-Hiai inequalities for $A\natural_t B$ and some other consequences.

Keywords

inequalities for means operator theory on hilbert spaces numerical range

Cite

@article{arxiv.2111.03256,
  title  = {Operator Spectral Geometric Versus Geometric Mean},
  author = {Hamid Reza Moradi and Shigeru Furuichi and Mohammad Sababheh},
  journal= {arXiv preprint arXiv:2111.03256},
  year   = {2023}
}

Comments

The coefficients in Theorem 2.2 and Corollary 2.3 have been changed. To appear in LAMA

Operator Spectral Geometric Versus Geometric Mean

Abstract

Keywords

Cite

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