Extremality of numerical radii of tensor products of matrices

Hwa Long Gau, Yueh Hua Lu

研究成果: 雜誌貢獻期刊論文同行評審

1 引文 斯高帕斯(Scopus)

摘要

For n-by-n and m-by-m complex matrices A and B, respectively, it is known that the inequality w(A⊗B)≤‖A‖w(B) holds, where w(⋅) and ‖⋅‖ denote, respectively, the numerical radius and the operator norm of a matrix. In this paper, we consider when this becomes an equality. We show that the equality w(A⊗B)=‖A‖w(B) holds if and only if A and B have k-by-k compressions A1 and B1, respectively, such that rank(‖A‖2Ik−A1 A1)≤minθ∈R⁡dim⁡ker⁡(w(B)Ik−Re(eB1)). We also give some consequences of this result. In particular, we show that if rankB≤sup⁡{k∈N:‖Ak‖=‖A‖k}, then w(A⊗B)=‖A‖w(B).

原文???core.languages.en_GB???
頁(從 - 到)82-98
頁數17
期刊Linear Algebra and Its Applications
565
DOIs
出版狀態已出版 - 15 3月 2019

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