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 Publication | Journal of Mathematical Analysis and Applications |
ISSN | 0022-247X |
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 | 10.1016/j.jmaa.2014.10.018 |
URL | View the original |
Language | 英语 |
Scopus ID | 2-s2.0-84922900689 |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | University of Macau |
Affiliation | 1.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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