Related papers: Numerical radii of accretive matrices
We obtain several norm and eigenvalue inequalities for positive matrices partitioned into four blocks. The results involve the numerical range of the off-diagonal block X, especially the distance from 0 to W(X).
In this work we show how to approach the problem of manimulating the numerical range of a unitary matrix. This task has far-reaching impact on the study of discrimination of quantum measurements. We achieve the aforementioned manipulation…
In this article, we prove an inner product inequality for Hilbert space operators. This inequality, then, is utilized to present a general numerical radius inequality using convex functions. Applications of the new results include obtaining…
The boundary of a numerical range of a finite matrix is always a nice curve (algebraic, closed and simple), but the equation it satisfies is often very complicated. We will show that, furthermore, there is no hope of describing these curves…
We develope new lower bounds for the $A$-numerical radius of semi-Hilbertian space operators, and applying these bounds we obtain upper bounds for the $A$-numerical radius of the commutators of operators. The bounds obtained here improve on…
For many applications, it is convenient to have good upper bounds for the norm of the inverse of a given matrix. In this paper, we obtain such bounds when A is a Nekrasov matrix, by means of a scaling matrix transforming A into a strictly…
Employing the Orlicz functions we extend the Buzano's inequality which is a refinement of the Cauchy-Schwarz inequality. Also using the Orlicz functions we obtain several numerical radius inequalities for a bounded linear operator as well…
We observe that the classical notion of numerical radius gives rise to a notion of smoothness in the space of bounded linear operators on certain Banach spaces, whenever the numerical radius is a norm. We demonstrate an important class of…
Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.
It is known that every closed curve of length \leq 4 in R^n (n>0) can be surrounded by a sphere of radius 1, and that this is the best bound. Letting S denote the circle of circumference 4, with the arc-length metric, we here express this…
Numerical relativity is an essential tool for solving Einstein's equations of general relativity for dynamical systems characterized by high velocities and strong gravitational fields. The implementation of new algorithms that can solve…
We define a new numerical range of an n\timesn complex matrix in terms of correlation matrices and develop some of its properties. We also define a related numerical range that arises from Alain Connes' famous embedding problem.
The number of non-negative integer matrices with given row and column sums appears in a variety of problems in mathematics and statistics but no closed-form expression for it is known, so we rely on approximations of various kinds. Here we…
In this article, we proved upper bounds for numerical radius of bounded linear operator and product of operators which generalize and improve existing inequalities. We also obtain a numerical radius inequality of invertible operator using…
In this paper, we achieve new and improved numerical radius inequalities of operators defined on a Hilbert space by using Orlicz function and Hermite-Hadamard inequality. The upper bounds of various inequalities involving numerical radii…
An expression for the subdifferential of the joint numerical radius is obtained. Its applications to the best approximation problems in the joint numerical radius are discussed.
We develop a number of inequalities to obtain bounds for the numerical radius of a bounded linear operator defined on a complex Hilbert space using the properties of $t$-Aluthge transform. We show that the bounds obtained are sharper than…
Krylov subspace methods are a powerful tool for efficiently solving high-dimensional linear algebra problems. In this work, we study the approximation quality that a Krylov subspace provides for estimating the numerical range of a matrix.…
They proved several properties and introduced some inequalities. We continue with the study of this generalized numerical radius and we develop diverse inequalities involving w_N. We also study particular cases with a fixed N(.), for…
On Hadamard manifolds, the radial fields, which are the negative gradients of the Busemann functions, can be used to designate a canonical sense of direction. This could have many potential applications to Hadamard manifold-valued data, for…