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On weakly unitarily invariant norm and the Aluthge transformation

โœ Scribed by K. Okubo

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
85 KB
Volume
371
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

In this paper we show that

where T โˆˆ B(H), ||| โ€ข ||| is a semi-norm on B(H) which satisfies some conditions, T = UP (polar decomposition), 0 ฮป 1 and f is a polynomial. As a consequence of this fact, we will show that some semi-norms ||| โ€ข ||| including the ฯ-radii (0 < ฯ 2) satisfy the inequality |||f (P ฮป UP 1-ฮป )||| |||f (T )|||. We also give some related results.

๐Ÿ“œ SIMILAR VOLUMES

On weakly unitarily invariant norm and t
On weakly unitarily invariant norm and the ฮป-Aluthge transformation for invertible operator
โœ Kazuyoshi Okubo ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 96 KB

Let T โˆˆ B(H) be an invertible operator with polar decomposition T = UP and B โˆˆ B(H) commute with T . In this paper we prove that |||P ฮป BUP 1-ฮป ||| |||BT |||, where ||| โ€ข ||| is a weakly unitarily invariant norm on B(H) and 0 ฮป 1. As the consequence of this result, we have |||f (P ฮป UP 1-ฮป )||| |||f

Perturbation bounds for weighted polar d
Perturbation bounds for weighted polar decomposition in the weighted unitarily invariant norm
โœ Hu Yang; Hanyu Li ๐Ÿ“‚ Article ๐Ÿ“… 2008 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 132 KB

## Abstract In this paper, by generalizing the ideas of the (generalized) polar decomposition to the weighted polar decomposition and the unitarily invariant norm to the weighted unitarily invariant norm, we present some perturbation bounds for the generalized positive polar factor, generalized non