Abstract Let ( I , ⦀ . ⦀ ) be a norm ideal of operators equipped with a unitarily invariant norm ⦀ . ⦀ . We exploit integral representations of certain functions to prove that certain ratios of… Expand

For any unitarily invariant norm on Hilbert-space operators, we prove Holder and Cauchy–Schwarz inequalities. As a consequence, several inequalities are lifted to the operator settings. Some more… Expand

Let p1<p2<⋯<pn be positive numbers, then for any integer m the Loewner matrix associated with the function xm is given by Lm=(pim−pjm)/(pi−pj)i,j=1n. A question was left open in a paper [Bhatia R, ...

Let p 1 , p 2 , … , p n be distinct positive real numbers and m be any integer. Every symmetric polynomial f ( x , y ) ∈ C [ x , y ] induces a symmetric matrix f ( p i , p j ) i , j = 1 n . We obta...

Let $$f:[0,\infty )\rightarrow [0,\infty )$$f:[0,∞)→[0,∞) be an operator monotone function and $$g: \mathbb {R}\rightarrow [0,\infty )$$g:R→[0,∞) be a conditionally negative definite(in short cnd)… Expand

In this article, we present several inequalities treating operator means and the Cauchy–Schwarz inequality. In particular, we present some new comparisons between operator Heron and Heinz means,… Expand