A numerical radius version of the arithmetic-geometric mean of operators

Abstract

In this paper, we obtain some numerical radius inequalities for operators, in particular for positive definite operators A; B a numerical radius and some operator norm versions for arithmeticgeometric mean inequality are obtained, respectively as ?2(A#B)? ? (A2+B2/2)- 1/2inf ||x||=1 ?(x), where ?(x) = ?(A - B)x,x?2, and ||A||||B|| ? 1/2 (||A2||+||B2||)-1/2 inf ||x||=||y||=1 ?(x,y), where, ?(x,y) = (?Ay,y? - ?Bx,x?)2.