Operator Monotone Functions which Are Defined Implicitly and Operator Inequalities
✍ Scribed by Mitsuru Uchiyama
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 152 KB
- Volume
- 175
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
✦ Synopsis
The function t : (0<:<1) is operator monotone on 0 t< . This is known as the Lo wner Heinz inequality. However, not too many examples of concrete operator monotone functions are known so far. We will systematically seek operator monotone functions which are defined implicitly. This investigation is new, and our method seems to be powerful. We will actually find a family of operator monotone functions which includes t : (0<:<1). Moreover, by constructing one-parameter families of operator monotone functions, we will get many operator inequalities; especially, we will extend the Furuta inequality and the exponential inequality of Ando.