New numerical radius inequalities for certain operator matrices

Studia Mathematica, 2012

We derive several numerical radius inequalities for 2×2 operator matrices. Numerical radius inequalities for sums and products of operators are given. Applications of our inequalities are also provided.

Tamkang Journal of Mathematics

The main purpose of this paper is to give an improvement of numerical radius inequality for an upper triangular operator matrix.

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

Linear and Multilinear Algebra, 2020

arXiv: Functional Analysis, 2020

Let ($\mathcal{H}, \langle . , .\rangle )$ be a complex Hilbert space and $A$ be a positive bounded linear operator on it. Let $w_A(T)$ be the $A$-numerical radius and $\|T\|_A$ be the $A$-operator seminorm of an operator $T$ acting on the semi-Hilbertian space $(\mathcal{H}, \langle .,.\rangle_A),$ where $\langle x, y\rangle_A:=\langle Ax, y\rangle$ for all $x,y\in \mathcal{H}$. In this article, we establish several upper and lower bounds for $B$-numerical radius of $2\times 2$ operator matrices, where $B=\begin{bmatrix} A & 0 0 & A \end{bmatrix}$. Further, we prove some refinements of earlier $A$-numerical radius inequalities for operators.

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.

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.

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.

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.

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).