On upper and lower bounds of the numerical radius and an equality condition

被引：204

作者：

Yamazaki, Takeaki ^{[1
]}

机构：

[1] Kanagawa Univ, Dept Math, Yokohama, Kanagawa 2218686, Japan

来源：

STUDIA MATHEMATICA | 2007年 / 178卷 / 01期

关键词：

numerical radius; Aluthge transform; normaloid operators;

D O I：

10.4064/sm178-1-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give an inequality relating the operator norm of T and the numerical radii of T and its Aluthge transform. It is a more precise estimate of the numerical radius than Kittaneh's result [Studia Math. 158 (2003)]. Then we obtain an equivalent condition for the numerical radius to be equal to half the operator norm.

引用

页码：83 / 89

页数：7

共 11 条

[1] Some generalized theorems on p-hyponormal operators [J].

Aluthge, A .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 1996, 24 (04) :497-501

[2] Aluthge transforms and the convex hull of the eigenvalues of a matrix [J].

Ando, T .

LINEAR & MULTILINEAR ALGEBRA, 2004, 52 (3-4) :281-292

[3]

[Anonymous], 1997, NUMERICAL RANGE

[4] Inner derivations and norm equality [J].

Barraa, M ;

Boumazgour, M .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (02) :471-476

[5]

FURUTA T., 2001, Invitation to Linear Operators

[6]

HEINZ E., 1951, Math. Ann., V123, P415

[7]

Jung IB, 2000, INTEGR EQUAT OPER TH, V37, P437

[8] A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix [J].

Kittaneh, F .

STUDIA MATHEMATICA, 2003, 158 (01) :11-17

[9] Numerical range of Aluthge transform of operator [J].

Wu, PY .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 357 (1-3) :295-298

[10] An expression of spectral radius via Aluthge transformation [J].

Yamazaki, T .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (04) :1131-1137

← 1 2 →