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 |
Remarks on the Grunsky norm and pth root transformation
โ Scribed by Arcadii Z Grinshpan
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 61 KB
- Volume
- 105
- Category
- Article
- ISSN
- 0377-0427
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
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
Scopolamine and hyoscyamine are tropane alkaloids employed in medicine as antispasmodics, preoperative medication and for the treatment of motion sickness. Since their chemical synthesis is difficult and expensive, these compounds are still extracted from plants that belong to several species of the