Recent advances on Furuta type operator inequalities

摘要

In 1987, Professor Takayuki Furuta established the so-called Furuta inequality which is an essential extension of the famous Loewner-Heinz inequality found in 1934, this paper is to give a short summary on recent advances on Furuta type operator inequalities. Emphasis is put on the complete form of Furuta inequality, Furuta type operator value function and some related applications.