Study on operator inequalities based on various analytic methods

点击翻译按钮获取中文摘要

To get norm comparison results for operator means we have to check positive definiteness of ratios of relevant means. By computing Fourier transforms we have checked positive definiteness of a variety of ratios. We have also made use of the concept of infinite divisibility to establish this for some ratios whose explicit computations of Fourier transforms seem hopeless.On the other hand, our technique was proved useful for study on completely positive maps appearing naturally in quantum information theory.