On Numerical Radius Inequalities for Operator Matrices

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.

Integral Equations and Operator Theory, 2011

We prove several numerical radius inequalities for certain 2×2 operator matrices. Among other inequalities, it is shown that if X, Y, Z, and W are bounded linear operators on a Hilbert space, then Mathematics Subject Classification (2010). 47A12, 47A30, 47A63, 47B15.

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.

Linear and Multilinear Algebra, 2020

In this article, we obtain some upper bounds for A-numerical radius of operators in semi-Hilbertian spaces which improve the existing ones. Furthermore, we discuss some generalizations of earlier Anumerical radius inequalities. We also establish several inequalities for B-numerical radius of n × n operator matrices, where B is an n × n diagonal matrix whose diagonal entries are positive operator A.

Journal of Mathematical Inequalities, 2016

In this article, we give several inequalities involving powers numerical radii and the usual operator norms of Hilbert space operators. In particular, if A i , B i and X i are bounded linear operators (i = 1,2,••• ,n ∈ N) , then we estimate the norm as well as the numerical radius to ∑ n i=1 X i A m i B i for some m ∈ N .

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).

Results in Mathematics

Let H be a complex Hilbert space and let A be a positive operator on H. We obtain new bounds for the A-numerical radius of operators in semi-Hilbertian space B A (H) that generalize and improve on the existing ones. Further, we estimate bounds for the B-operator seminorm and B-numerical radius of 2 × 2 operator matrices, where B = diag(A, A). The bounds obtained here improve on the existing bounds.

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

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.

In this paper, it is shown, among other inequalities, that if A, B ∈ B(H), then, for p 1, we have 2 1 p-2 |A * | 2 + |B| 2 p 2 1 p-3