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Elementary operators and the Aluthge transform

โœ 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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๐Ÿ“œ SIMILAR VOLUMES


On weakly unitarily invariant norm and t
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

ฮป-Aluthge transforms and Schatten ideals
โœ Jorge Antezana; Pedro Massey; Demetrio Stojanoff ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 329 KB
On weakly unitarily invariant norm and t
โœ K. Okubo ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 85 KB

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 |

On generalized numerical range of the Al
โœ Masatoshi Ito; Hiroshi Nakazato; Kazuyoshi Okubo; Takeaki Yamazaki ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 130 KB

In this paper the authors show that the Aluthge transformation T of a matrix T and a polynomial f satisfy the inclusion relation W C (f ( T )) โŠ‚ W C (f (T )) for the generalized numerical range if C is a Hermitian matrix or a rank-one matrix.

Rank one operators and norm of elementar
โœ Ameur Seddik ๐Ÿ“‚ Article ๐Ÿ“… 2007 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 141 KB

Let A be a standard operator algebra acting on a (real or complex) normed space E. For two n-tuples A = (A 1 , . . . , A n ) and B = (B 1 , . . . , B n ) of elements in A, we define the elementary operator R A,B on A by the relation R A,B (X) = n i=1 A i XB i for all X in A. For a single operator A