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Spectral radius, numerical radius, and the product of operators
Alizadeh,Rahim1; Asadi,Mohammad B.2; Cheng,Che Man3; Hong,Wanli3; Li,Chi Kwong4
2015
Source PublicationJournal of Mathematical Analysis and Applications
ISSN0022-247X
Volume423Issue:1Pages:639-645
AbstractLet 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
DOI10.1016/j.jmaa.2014.10.018
URLView the original
Language英语
Scopus ID2-s2.0-84922900689
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.Department of Mathematics, Shahed University,Tehran,P.O. Box 18151-159,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
4.Department of Mathematics, College of William and Mary,Williamsburg,23187,United States
Recommended Citation
GB/T 7714
Alizadeh,Rahim,Asadi,Mohammad B.,Cheng,Che Man,et al. Spectral radius, numerical radius, and the product of operators[J]. Journal of Mathematical Analysis and Applications,2015,423(1):639-645.
APA Alizadeh,Rahim,Asadi,Mohammad B.,Cheng,Che Man,Hong,Wanli,&Li,Chi Kwong.(2015).Spectral radius, numerical radius, and the product of operators.Journal of Mathematical Analysis and Applications,423(1),639-645.
MLA Alizadeh,Rahim,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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