Some extensions of the Young and Heinz inequalities for Matrices

2017/05/07 by Hajmohamadi, Monire, Lashkaripour, Rahmatollah, Bakherad, Mojtaba
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1705.02585

Abstract

In this paper, we present some extensions of the Young and Heinz inequalities for the Hilbert-Schmidt norm as well as any unitarily invariant norm. Furthermore, we give some inequalities dealing with matrices. More precisely, for two positive semidefinite matrices A and B we show that ‖A^νXB^1-ν+A^1-νXB^ν‖₂²≤‖AX+XB‖₂²- 2r‖AX-XB‖₂²-r₀(‖A^(1)/(2)XB^(1)/(2)-AX‖₂²+ ‖A^(1)/(2)XB^(1)/(2)-XB‖₂²), where X is an arbitrary n× n matrix, 0

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