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Spectral radius, numerical radius, and the product of operators
Rahim Alizadeh1; Mohammad B.Asadi2; Che-Man Cheng3; Wanli Hong3; Chi-Kwong Li4
2015
Source PublicationJournal of Mathematical Analysis and Applications
ISSN1096-0813
Volume423Issue:1Pages:639-645
Abstract

Let σ(A), ρ(A) and r(A) denote the spectrum, spectral radius and numerical radius of a bounded linear operator A on a Hilbert space H, respectively. We show that a linear operator A satisfiesρ(AB)≤r(A)r(B)for all bounded linear operators B if and only if there is a unique μ∈σ(A) satisfying |μ|=ρ(A) and A=μ(I+L)/2 for a contraction L with 1∈σ(L). One can get the same conclusion on A if ρ(AB)≤r(A)r(B) for all rank one operators B. If H is of finite dimension, we can further decompose L as a direct sum of C⊕0 under a suitable choice of orthonormal basis so that Re(Cx, x)≥1 for all unit vector x.

KeywordNumerical Radius Product Of Operators Spectral Radius
DOIhttps://doi.org/10.1016/j.jmaa.2014.10.018
URLView the original
Indexed BySCIE
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000349706000038
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorChe-Man Cheng
Affiliation1.Department of Mathematics, Shahed University, P.O. Box 18151-159, Tehran, Iran
2.School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
3.Department of Mathematics, University of Macau, Macao, China
4.Department of Mathematics, College of William and Mary, Williamsburg, VA 23187, USA
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Rahim Alizadeh,Mohammad B.Asadi,Che-Man Cheng,et al. Spectral radius, numerical radius, and the product of operators[J]. Journal of Mathematical Analysis and Applications,2015,423(1):639-645.
APA Rahim Alizadeh,Mohammad B.Asadi,Che-Man Cheng,Wanli Hong,&Chi-Kwong Li.(2015).Spectral radius, numerical radius, and the product of operators.Journal of Mathematical Analysis and Applications,423(1),639-645.
MLA Rahim Alizadeh,et al."Spectral radius, numerical radius, and the product of operators".Journal of Mathematical Analysis and Applications 423.1(2015):639-645.
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