Mojtaba Bakherad - Department of Mathematics, Faculty of Mathematics,University of Sistan and Baluchestan, Zahedan, Iran.

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( )

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