An Operator Inequality and Matrix NormalityLinear Algebra and its Applications
AbstractLet A be a bounded linear operator on a Hilbert space H; denote |A| = (A∗A)12and the norm of x ϵ H by ‖x‖. It is proved that |(Au, v)|≤⦀A|au‖ ⦀A∗|1−a‖ ∀u, v ϵ H for any 0 < α < 1. In particular, |(Au, v)|≤(|A|u, u)12(|A∗|v,v)12 ∀u, v ϵ H. When H is of finite dimension, it is shown that A must be a normal operator if it satisfies |(Au, u)|≤(|A|u, u)a(|A∗|u, u)1−a ∀u ϵ H for some real number α ≠ 12.
Citation InformationCharles R Johnson and Fuzhen Zhang. "An Operator Inequality and Matrix Normality" Linear Algebra and its Applications Vol. 240 (1996) p. 105 - 110 ISSN: 0024-3795
Available at: http://works.bepress.com/fuzhen-zhang/15/