๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On generalized numerical range of the Aluthge transformation

โœ Scribed by Masatoshi Ito; Hiroshi Nakazato; Kazuyoshi Okubo; Takeaki Yamazaki

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
130 KB
Volume
370
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

โœฆ Synopsis

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.

๐Ÿ“œ SIMILAR VOLUMES

On weakly unitarily invariant norm and t
On weakly unitarily invariant norm and the Aluthge transformation
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 the Hu-Hurley-Tam conjecture concerni
On the Hu-Hurley-Tam conjecture concerning the generalized numerical range
โœ Che-Man Cheng; Chi-Kwong Li ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 102 KB

Suppose m and n are integers such that 1 m n, and H is a subgroup of the symmetric group S m of degree m. Define the generalized matrix function associated with the principal character of the group H on an m ร— m matrix B = (b ij ) by b jฯƒ (j) , and define the generalized numerical range of an n ร— n

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