Numerical radius inequalities for 2×2 operator matrices

Proyecciones (Antofagasta), 2012

In this paper we prove some upper and lower bounds for the numerical radius of the off-diagonal part of 3 × 3 operator matrices and some bounds for the numerical radius inequalities of the general 3 × 3 operator matrix.

Advances in Difference Equations

In this work, we provide upper and lower bounds for the numerical radius of an n × n off-diagonal operator matrix, which extends some results by Abu-Omar and Kittaneh

2019

We present new upper and lower bounds for the numerical radius of a bounded linear operator defined on a complex Hilbert space, which improve on the existing bounds. We also obtain some upper and lower bounds for the numerical radius of operator matrices and illustrate with numerical examples that these bounds are better than the existing bounds.

arXiv (Cornell University), 2017

We generalize several inequalities involving powers of the numerical radius for off-diagonal part of 2 × 2 operator matrices of the form T = 0 B

Filomat, 2020

We present some inequalities related to the Hilbert-Schmidt numerical radius of 2 x 2 operator matrices. More precisely, we present a formula for the Hilbert-Schmidt numerical radius of an operator as follows: w2(T) = sup ?2+?2=1 ||?A + ?B||2, where T = A + iB is the Cartesian decomposition of T ? HS(H).

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.

arXiv: Functional Analysis, 2019

Let $A$ be a positive operator on a complex Hilbert space $\mathcal{H}.$ We present inequalities concerning upper and lower bounds for $A$-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 $B$-numerical radius of $2\times 2$ operator matrices where $B$ is the $2\times 2$ diagonal operator matrix whose diagonal entries are $A$. Further we obtain upper bounds for $A$-numerical radius for product of operators which improve on the existing bounds.

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.

Linear Algebra and its Applications, 2019

We prove several Hilbert-Schmidt numerical radius inequalities for operator matrices. A refinement of the triangle inequality for the Hilbert-Schmidt norm is also given.

Annals of Functional Analysis, 2021

The main goal of this article is to establish several new-numerical radius equalities for n × n circulant, skew circulant, imaginary circulant, imaginary skew circulant, tridiagonal, and anti-tridiagonal operator matrices, where is the n × n diagonal operator matrix whose diagonal entries are positive bounded operator A. Some special cases of our results lead to the results of earlier works in the literature, which shows that our results are more general. Further, some pinching type-numerical radius inequalities for n × n block operator matrices are given. Some equality conditions are also given. We also provide a concluding section, which may lead to several new problems in this area.