Contractive maps on operator ideals and norm inequalities

Norm Inequalities Related to the Heron and Heinz Means

“…Moreover, it is proved that |||A ν XB 1−ν − A 1−ν XB ν ||| is a convex function of ν; see [10,Remark 3.12]. These results have also been proved in matrix version by several authors; see [12,18] for example.…”

“…Further in [10], authors proved some generalizations of the difference version of Heinz inequality, given by…”

Norm inequalities related to the Heinz means

“…We use X 1 and Y 1 to denote two selfadjoint operators in B(H) and D = L X 1 -R Y 1 . The following proposition is a result for a contractive map in I; for more details refer to [10]. (1)…”

“…, this is a convex function, its minimum value is α( 1 2 ) = 0, and its maximum value is α(0) = α(1) = 1. In [10] the authors have presented the result that…”

Norm inequalities related to Heinz and Heron operator means

“…Heretofore the inequalities discussed above are proved in the setting of matrices. Kapil and Singh in [3], using the contractive maps proved that the relation (1.2) holds for positive definite operators on a complex Hilbert space H. They also proved that if A, B and X are bounded linear operators on H and A, B are positive definite operators and α ∈ [ 1 2 , ∞), then…”