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Article
An Operator Inequality and Matrix Normality
Linear Algebra and its Applications
  • Charles R Johnson, College of William and Mary
  • Fuzhen Zhang, University of California, Santa Barbara
Document Type
Article
Publication Date
6-1-1996
Disciplines
Abstract
Let 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.
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DOI
10.1016/0024-3795(94)00189-8
Citation Information
Charles 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/