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- Title
Some Extensions of the Young and Heinz Inequalities for Matrices.
- Authors
Hajmohamadi, M.; Lashkaripour, R.; Bakherad, M.
- 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 ‖AνXB1-ν+A1-νXBν‖22≤‖AX+XB‖22-2r‖AX-XB‖22-r0‖A12XB12-AX‖22+‖A12XB12-XB‖22,<graphic></graphic>where X is an arbitrary n×n<inline-graphic></inline-graphic> matrix, 0<ν≤12<inline-graphic></inline-graphic>, r=min{ν,1-ν}<inline-graphic></inline-graphic> and r0=min{2r,1-2r}<inline-graphic></inline-graphic>.
- Subjects
RING extensions (Algebra); MATHEMATICAL inequalities; MATRICES (Mathematics); SEMIDEFINITE programming; CONVEX functions
- Publication
Bulletin of the Iranian Mathematical Society, 2018, Vol 44, Issue 4, p977
- ISSN
1018-6301
- Publication type
Article
- DOI
10.1007/s41980-018-0064-3