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- W2103516256 abstract "Let A,B∈B(H) be such that 0<b1I⩽A⩽a1I and 0<b2I⩽B⩽a2I for some scalars 0<bi<ai,i=1,2 and Φ:B(H)→B(K) be a positive linear map. We show that for any operator mean σ with the representing function f, the double inequalityω1-α(Φ(A)#αΦ(B))⩽(ωΦ(A))∇αΦ(B)⩽αμΦ(AσB)holds, where μ=a1b1(f(b2a1-1)-f(a2b1-1))b1b2-a1a2, ν=a1a2f(b2a1-1)-b1b2f(a2b1-1)a1a2-b1b2, ω=αν(1-α)μ and #α (∇α, resp.) is the weighted geometric (arithmetic, resp.) mean for α∈(0,1). As applications we present several generalized operator inequalities including Diaz–Metcalf and reverse Ando type inequalities. We also give some related inequalities involving Hadamard product and operator means." @default.
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- W2103516256 date "2012-08-01" @default.
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- W2103516256 title "A general double inequality related to operator means and positive linear maps" @default.
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- W2103516256 doi "https://doi.org/10.1016/j.laa.2012.03.029" @default.
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