A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix

By F. Kıttaneh. 2003

331 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2be4ce0a00e80cb9754f7bab4eb3b0ee901e619d

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

More accurate numerical radius inequalities (I) (2019, background): “er bounds in (1.1). We refer the reader to [10, 12, 13] for a sample of such research. In [7], Kittaneh proved (1.2) 1 4 kA ∗A+AA k ≤ w2(A) ≤ 1 2 kA∗A+AA k. He also proved the following inequality in [6] w(A) ≤ 1 2 k |A|+|A∗| k and the inequality is reversed if 1 2 is replaced by 1 4 . In fact, noti”
Upper and lower bounds for the numerical radius with an application to involution operators (2015, background): “Kittaneh has shown in [5, 7], respectively, that, if A ∈ B(H), then”
On upper and lower bounds of the numerical radius and an equality condition (2007, methodology): “2) and [8] that is, if $T^{2}=0$ , then $w(T)= \frac{1}{2}||T||$ .”
Development of inequalities and characterization of equality conditions for the numerical radius (2021, background): “Over the years various reﬁnements of (1.1) have been obtained, we refer the interested readers to see [1, 4, 5, 7, 12, 13, 15] and the references therein.”
Bounds for the zeros of polynomials from matrix inequalities (2003, result): “This is a continuation of our earlier work [10] and [ 13 ].”
Spectral radius inequalities for Hilbert space operators (2005, methodology): “We remark that the inequalities (20) and (21) can also be obtained by employing Theorem 1 in [4], the numerical radius counterparts of the pinching inequalities (18) and (19), and the fact that the spectral radius of an operator is dominated by its numerical radius.”
Power Inequalities for the Numerical Radius of a Product of Two Operators in Hilbert Spaces (2024, neutral): “It is well known that (see for instance [15]) if P is a positive operator and q ∈ (0, 1] then for any u ∈ H, ‖u‖ = 1, we have 〈P u, u〉 ≤ 〈Pu, u〉 .”