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Volume 45 Number 5

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Research articles

ScienceAsia 45(2019): 488-493 |doi: 10.2306/scienceasia1513-1874.2019.45.488


A note on equivalence of some Rotfel’d type theorems


Yaxin Gao, Chaojun Yang, Fangyan Lu*

 
ABSTRACT:     In this note, we prove that some of recent Rotfel’d type inequalities are equivalent, which is an extension of Huang, Wang and Zhang [Linear Multilinear Algebra 66 (2018) 1626–1632]. Among other results, it is shown that if ƒ : [0,∞) → [0,∞) is a concave function and A ∈ 𝕄2(𝕄n) is a normal matrix with its numerical range contained in a sector: S α = {z ∈ ℂ : Re z ≥ 0,|lm z| (Re z)tan α} for some α ∈ [0, π/2 ), then ƒ ||(|A|)|| ≤ 2 || ƒ (sec α/2 |A11 + A22|)|| for any unitarily invariant norm ||·||. This inequality improves a recent result of Zhao and Ni [Linear Multilinear Algebra 66 (2018) 410–417].

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a Department of Mathematics, Soochow University, Suzhou 215006 China

* Corresponding author, E-mail: fylu@suda.edu.cn

Received 1 Apr 2019, Accepted 30 Oct 2019