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GENERALIZATIONS OF HEINZ MEAN OPERATOR INEQUALITIES INVOLVING POSITIVE LINEAR MAP.
- Source :
-
Journal of Computational Analysis & Applications . 11/15/2017, Vol. 23 Issue 6, p1089-1096. 8p. - Publication Year :
- 2017
-
Abstract
- In this paper, we study the Heinz mean inequalities of two positive operators involving positive linear map. We obtain a generalized conclusion based on operator Diaz-Metcalf type inequality. The conclusion is presented as follows: Let Φ be a unital positive linear map, if 0 < m1 2 ≤ A ≤ M1 2 and 0 < m2 2 ≤ B ≤ M22 for some positive real numbers m1 ≤ M1, m2 ≤ M2, then for α ϵ [0; 1] and p ≥ 2, the following inequality holds : ( M2m2/ M1m1 Φ(A) + Φ(B))p ≤2-(p+4) [M2m2(M1 2 + m1 2) +M1m1(M2 2 + m2 2) /min{(M1m1) 3-α/2 (M2m2) 1+α/2, (M1m1) 2+α/2 (M2m2)2-α/2}2p Φp(Hα(A;B)). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15211398
- Volume :
- 23
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 121182551