Numerical Radius Inequalities for Square-zero and Idempotent Operators
Hwa-Long Gau, Chin-Ying Huang, Pei Yuan Wu · Operators and Matrices · 2008
We show that if A is a square-zero or an idempotent operator on a Hilbert space and B commutes with A , then w(AB) min{w(A) B , A w(B)} holds, where w() and denote, respectively, the numerical radius and operator norm of an operator Mathematics subject classification (2000): 47A12.