Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897743 | Linear Algebra and its Applications | 2018 | 17 Pages |
Abstract
For an n-by-n matrix A, let w(A) and âAâ denote its numerical radius and operator norm, respectively. The following three inequalities, each a strengthening of w(A)â¤âAâ, are known to hold: w(A)2â¤(âAâ2+w(A2))/2, w(A)â¤(âAâ+âA2â1/2)/2, and w(A)â¤(âAâ+w(Ît(A)))/2 (0â¤tâ¤1), where Ît(A) is the generalized Aluthge transform of A. In this paper, we derive necessary and sufficient conditions in terms of the operator structure of A for which the inequalities become equalities.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Hwa-Long Gau, Pei Yuan Wu,