| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4603872 | Linear Algebra and its Applications | 2006 | 5 Pages |
Abstract
Let T∈B(H) be an invertible operator with polar decomposition T = UP and B∈B(H) commute with T. In this paper we prove that ∣∣∣PλBUP1−λ∣∣∣ ⩽ ∣∣∣BT∣∣∣, where ∣∣∣ · ∣∣∣ is a weakly unitarily invariant norm on B(H) and 0 ⩽ λ ⩽ 1. As the consequence of this result, we have ∣∣∣f(PλUP1−λ)∣∣∣ ⩽ ∣∣∣f(T)∣∣∣ for any polynomial f.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
