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On weakly unitarily invariant norm and the λ-Aluthge transformation for invertible operator

✍ Scribed by Kazuyoshi Okubo

Publisher: Elsevier Science
Year: 2006
Tongue: English
Weight: 96 KB
Volume: 419
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.04.003

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✦ Synopsis

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 |||P λ BUP 1-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 (P λ UP 1-λ )||| |||f (T )||| for any polynomial f .

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✍ K. Okubo 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 85 KB

In this paper we show that where T ∈ B(H), ||| • ||| is a semi-norm on B(H) which satisfies some conditions, T = UP (polar decomposition), 0 λ 1 and f is a polynomial. As a consequence of this fact, we will show that some semi-norms ||| • ||| including the ρ-radii (0 < ρ 2) satisfy the inequality |