Spectral radius, numerical radius, and the product of operators | |
Rahim Alizadeh1; Mohammad B.Asadi2; Che-Man Cheng3; Wanli Hong3; Chi-Kwong Li4 | |
2015 | |
Source Publication | Journal of Mathematical Analysis and Applications |
ISSN | 1096-0813 |
Volume | 423Issue: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. |
Keyword | Numerical Radius Product Of Operators Spectral Radius |
DOI | https://doi.org/10.1016/j.jmaa.2014.10.018 |
URL | View the original |
Indexed By | SCIE |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000349706000038 |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | DEPARTMENT OF MATHEMATICS |
Corresponding Author | Che-Man Cheng |
Affiliation | 1.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 Affilication | University 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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