NUMERICAL RADIUS INEQUALITIES FOR PRODUCTS OF HILBERT SPACE OPERATORS

被引：9

作者：

Abu-Omar, Amer ^{[1
]}

Kittaneh, Fuad ^{[2
]}

机构：

[1] Philadelphia Univ, Dept Basic Sci & Math, Amman, Jordan

[2] Univ Jordan, Dept Math, Amman, Jordan

来源：

JOURNAL OF OPERATOR THEORY | 2014年 / 72卷 / 02期

关键词：

Numerical radius; operator norm; inequality; normal operator; self-adjoint operator; positive operator;

D O I：

10.7900/jot.2013jun12.1990

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

New numerical radius inequalities for products of two Hilbert space operators are given. Some of our inequalities improve well-known ones. Among other inequalities, it is shown that if A, B is an element of B (94), then w(AB) <= (parallel to A parallel to + D-A)w(B), where D-A = inf(z is an element of C)parallel to A - zI parallel to. Moreover, w(AB) <= parallel to A parallel to w(B) + (1/2)w(AB - BA*). In particular, if AB = BA*, then w(AB) <= parallel to A parallel to w(B).

引用

页码：521 / 527

页数：7

共 14 条

[1] A numerical radius inequality involving the generalized Aluthge transform [J].

Abu Omar, Amer ;

Kittaneh, Fuad .

STUDIA MATHEMATICA, 2013, 216 (01) :69-75

[2]

Abu-Omar A., ROCKY MOUNT IN PRESS

[3]

DAVIDSON KR, 1988, MICH MATH J, V35, P261

[4] UNITARILY-INVARIANT OPERATOR NORMS [J].

FONG, CK ;

HOLBROOK, JAR .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1983, 35 (02) :274-299

[5]

Gustafson K. E., 1997, NUMERICAL RANGE FIEL

[6]

Halmos P, 1982, HILBERT SPACE PROBLE

[7]

Hirzallah O, 2014, MATH SCAND, V114, P110

[8] Numerical Radius Inequalities for Certain 2 x 2 Operator Matrices [J].

Hirzallah, Omar ;

Kittaneh, Fuad ;

Shebrawi, Khalid .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2011, 71 (01) :129-147

[9] Numerical Radius Inequalities for Commutators of Hilbert Space Operators [J].

Hirzallah, Omar ;

Kittaneh, Fuad ;

Shebrawi, Khalid .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2011, 32 (07) :739-749

[10] Theory vs. Experiment: Multiplicative Inequalities for the Numerical Radius of Commuting Matrices [J].

Holbrook, John ;

Schoch, Jean-Pierre .

TOPICS IN OPERATOR THEORY: OPERATORS, MATRICES AND ANALYTIC FUNCTIONS, VOL 1, 2010, 202 :273-+

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