Numerical radius inequalities for Hilbert space operators (original) (raw)

Numerical radius inequalities for Hilbert space operators. II

Studia Mathematica, 2007

We give several sharp inequalities involving powers of the numerical radii and the usual operator norms of Hilbert space operators. These inequalities, which are based on some classical convexity inequalities for nonnegative real numbers and some operator inequalities, generalize earlier numerical radius inequalities.

Numerical Radius and Operator Norm Inequalities

Journal of Inequalities and Applications, 2009

A general inequality involving powers of the numerical radius for sums and products of Hilbert space operators is given. This inequality generalizes several recent inequalities for the numerical radius, and includes that if A and B are operators on a complex Hilbert space H, then w r A * B ≤ 1/2 |A| 2r |B| 2r for r ≥ 1. It is also shown that if X i is normal i 1, 2, . . . , n , then n i 1 X i r ≤ n r−1 n i 1 |X i | r . Related numerical radius and usual operator norm inequalities for sums and products of operators are also presented.

New Estimates on the Numerical Radius of Operators

m-hikari.com

In this paper we find new estimate for the numerical radius for sums and products of Hilbert space operators. Also we generalized and sharpened some recent inequalities for the numerical radius.

Numerical Radius Inequalities for Several Operators

and w(AB ± BA) ≤ 2 √ 2 B w 2 (A) − | Re A 2 − Im A 2 | 2 , where w(•) and • are the numerical radius and the usual operator norm, respectively. These inequalities generalize and refine some earlier results of Fong and Holbrook. Some applications of our results are given.

General Upper Bounds for the Numerical Radii of Powers of Hilbert Space Operators

The Eurasia Proceedings of Science Technology Engineering and Mathematics

In this paper, we will present several upper bounds for the numerical radii of a operator matrices. We use these bounds to generalize and improve some well-known numerical radius inequalities. We provide a refinement of an earlier numerical radius inequality due to (Bani-Domi & Kittaneh, 2021) [Norm and numerical radius inequalities for Hilbert space operators], (Bani-Domi & Kittaneh, 2021) [Refined and generalized numerical radius inequalities for operator matrices] and (Al-Dolat & Kittaneh, 2023) [Upper bounds for the numerical radii of powers of Hilbert space operators].

An alternative estimate for the numerical radius of Hilbert space operators

Mathematica Slovaca, 2020

We give an alternative lower bound for the numerical radii of Hilbert space operators. As a by-product, we find conditions such that \begin{array}{} \displaystyle \omega\left(\left[\begin{array}{cc} 0 & R \\ S & 0 \end{array}\right]\right)=\frac{\Vert R \Vert +\Vert S\Vert }{2} \end{array}$$ where R, S ∈ 𝔹(𝓗).

On inequalities for A-numerical radius of operators

arXiv: Functional Analysis, 2019

Let AAA be a positive operator on a complex Hilbert space mathcalH.\mathcal{H}.mathcalH. We present inequalities concerning upper and lower bounds for AAA-numerical radius of operators, which improve on and generalize the existing ones, studied recently in [A. Zamani, A-Numerical radius inequalities for semi-Hilbertian space operators, Linear Algebra Appl. 578 (2019) 159-183]. We also obtain some inequalities for BBB-numerical radius of 2times22\times 22times2 operator matrices where BBB is the 2times22\times 22times2 diagonal operator matrix whose diagonal entries are AAA. Further we obtain upper bounds for AAA-numerical radius for product of operators which improve on the existing bounds.

Further refinements of generalized numerical radius inequalities for Hilbert space operators

Georgian Mathematical Journal, 2019

In this paper, we show some refinements of generalized numerical radius inequalities involving the Young and Heinz inequality. In particular, we present w_{p}^{p}(A_{1}^{*}T_{1}B_{1},\dots,A_{n}^{*}T_{n}B_{n})\leq\frac{n^{1-\frac{1% }{r}}}{2^{\frac{1}{r}}}\bigg{\|}\sum_{i=1}^{n}[B_{i}^{*}f^{2}(|T_{i}|)B_{i}]^{% rp}+[A_{i}^{*}g^{2}(|T_{i}^{*}|)A_{i}]^{rp}\bigg{\|}^{\frac{1}{r}}-\inf_{\|x\|% =1}\eta(x), where {T_{i},A_{i},B_{i}\in\mathbb{B}(\mathscr{H})} {(1\leq i\leq n)} , f and g are nonnegative continuous functions on {[0,\infty)} satisfying {f(t)g(t)=t} for all {t\in[0,\infty)} , {p,r\geq 1} , {N\in\mathbb{N}} , and \displaystyle\eta(x)=\frac{1}{2}\sum_{i=1}^{n}\sum_{j=1}^{N}\Bigl{(}\sqrt[2^{j% }]{\big{\langle}(A_{i}^{*}g^{2}(|T_{i}^{*}|)A_{i})^{p}x,x\big{\rangle}^{2^{j-1% }-k_{j}}\big{\langle}(B_{i}^{*}f^{2}(|T_{i}|)B_{i})^{p}x,x\big{\rangle}^{k_{j}}} \displaystyle -\sqrt[2^{j}]{\big{\langle}(B_{i}^{*}f^{2}(|T_{i}|)B_{i}% )^{p}x,x\big{\rangle}^{k_{j}+1}\big{\langle}(A_{i}^{*}g^{2...

General Numerical Radius Inequalities

Studies in Mathematical Sciences, 2013

In this article, we establish new numerical radius inequalities for bounded linear operators on a complex Hilbert space. Also, we generalize some known inequalities.