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In this paper, we refine some operator inequalities as follows: Let A , B be positive operators on a Hilbert space with 0 < m A m′ < M′ B… Click to show full abstract
In this paper, we refine some operator inequalities as follows: Let A , B be positive operators on a Hilbert space with 0 < m A m′ < M′ B M . Then for every positive unital linear map Φ and p 1 , Φp(A tB)Φ((A tB)−1)+Φp((A tB)−1)Φp(A tB) (M +m)2p 2MpmpKμ p(h′) , and p 2 , Φ(A B) (K2(h)(M2 +m2)2 4 2 p K2μ (h′)M2m2 )p Φ(Ht(A,B)) for all t ∈ [0,1] , where μ = min{t,1− t} , K(h) = (h+1)2 4h , K(h′) = (h ′+1)2 4h′ , h = M m and h ′ = M′ m′ .
Keywords:
inequalities positive;
linear maps;
operator inequalities;
refinements operator;
positive linear;
operator
Journal Title: Journal of Mathematical Inequalities
Year Published: 2017
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Journal Title: Journal of Mathematical Inequalities
Year Published: 2017
Link to full text (if available)
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recommendations!