Let T โ B(H) be an invertible operator with polar decomposition T = UP and B โ B(H) commute with T . In this paper we prove that |||P ฮป BUP 1-ฮป ||| |||BT |||, where ||| โข ||| 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
Elementary operators and the Aluthge transform
โ Scribed by Fernanda Botelho; James Jamison
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 146 KB
- Volume
- 432
- Category
- Article
- ISSN
- 0024-3795
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๐ SIMILAR VOLUMES
In this paper we show that where T โ B(H), ||| โข ||| 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 ||| โข ||| including the ฯ-radii (0 < ฯ 2) satisfy the inequality |
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