NEW INEQUALITIES INVOLVING OPERATOR MEANS FOR SECTOR MATRICES

Document Type : Original Article

Author
Somayeh Malekinejad
Department of Mathematics, Payame Noor University, P.O. Box 193953697, Tehran, Iran.
10.22034/maco.3.2.6
Abstract
 The main goal of this paper is to discuss the famous inequalities from positive definite matrices to sector matrices in a more general setting. This includes the mean-convex inequality and Callebaut inequalitiy. Afterward, several inequalities involved positive linear map, are presented for sector matrices. For instance, we show that if A, B ∈ Sα are two sector matrices, then for all σ ≥ ♯ we have
R(Φ−1(AσB)) ≤ sec2 α R(Φ(A−1)♯Φ(B−1)).

Keywords

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Mathematical Analysis and Convex Optimization
Volume 3, Issue 2
December 2022
Pages 59-67