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Title of article :
Some functions reversing the order of positive operators Original Research Article
Author/Authors :
Josip Pe?ari?، نويسنده , , Jadranka Mi?i?، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2005
Pages :
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Abstract :
As a complement to our previous results about the function preserving the operator order, we shall show the following reversing version: Let A and B be positive operators on a Hilbert space H satisfying MI greater-or-equal, slanted B greater-or-equal, slanted mI > 0. Let f(t) be a continuous convex function on [m, M]. If g(t) is a continuous decreasing convex function on [m,M]union or logical sumSp(A), then for a given α > 0imagewhere β = maxmless-than-or-equals, slanttless-than-or-equals, slantM f(m) + (f(M) − f(m))(t − m)/(M − m) − αg(t) . Our main result is to classify complementary inequalities on power means of positive operators. As a matter of fact, we determine real constants α1 and α1 such that image if r less-than-or-equals, slant s, where image (rset membership, variantR-45 degree rule 0 ) is weighted power mean of positive operators Aj, Sp(Aj)subset of or equal to[m,M] for some scalars 0 < m < M and ωjset membership, variantR+ such that image (j = 1, … ,k).
Keywords :
Generalized Kantorovich constant , Mond–Pe?cari´c method , Weighted powermean , Operator order
Journal title :
Linear Algebra and its Applications
Link To Document :