Some families of operator norm inequalities

Abstract

It is known that the function $f(e^x)/g(e^x)$ is positive definite for some functions $f,g$ implies the operator norm inequality related to $f,g$. We treat functions which have the following form: $f(t)=t^{(1-{\sum }_{i=1}^n(a_i-b_i))/2}{\prod }_{i=1}^n\frac{b_i(t^{a_i}-1)}{a_i(t^{b_i}-1)}$.

21 pages