Noncommutative operator entropy

Let B H denote the C -algebra of all bounded linear operators on a complex Hilbert space H with the identity I H In this talk, we de ne noncommutative operatorentropy and present some operator inequalities. Among other inequalities, we show the following inequalties: ( ) In particular, ( ) are strictly positive operators such that( )is operator concave and( )

Keywords:

operator entropy , operator monotone function , Bochner integration , en-tropy inequality