$(\alpha,\beta)$-A-Normal Operators in Semi-Hilbertian Spaces
  In this paper we introduce and prove some properties of $(\alpha;\beta)$-normal operators according to semi-Hilbertian space structures. Furthermore we s,ate various inequalities between the A-operator norm and A-numerical radius of $(\alpha,\beta)$-normal operators in semi Hilbertian spaces. 
Abdelkader Benali and Ould Ahmed Mahmoud Sid Ahmed
math.FA