Abstract One of the basic assumptions in hub covering problems is considering the covering radius as an exogenous parameter which cannot be controlled by the decision maker. Practically and in many real world cases with a negligible increase in costs, to increase the covering radii, it is possible to save the costs of establishing additional hub nodes. Change in problem parameters during the pl...

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

In this paper, we are interested in studying Bishop–Phelps–Bollobás type properties related to the denseness of operators which attain their numerical radius. We prove that every Banach space with a micro-transitive norm and second index strictly positive satisfies point property, see one-dimensional is only one both 1 property. also consider two weaker Lp,p-nu Lo,o-nu, local versions operator ...

We apply numerical radius and spectral radius estimates to the Frobenius companion matrices of monic polynomials to derive new bounds for their zeros and give different proofs of some known bounds.

We present a conjecture which when true would generalize T. Ando's characterization of the numerical radius of (bounded linear) operators on a Hilbert space (see A]). Some evidence for the validity of the conjecture is given. In the nite dimensional case we shall restate the conjecture in terms of convex matrix sets and norms on matrices that are invariant under unitary similarities (u.s.i. nor...

Let m,n ≥ 2 be positive integers. Denote by Mm the set of m×m complex matrices and by w(X) the numerical radius of a square matrix X. Motivated by the study of operations on bipartite systems of quantum states, we show that a linear map φ : Mmn →Mmn satisfies w(φ(A⊗B)) = w(A⊗B) for all A ∈Mm and B ∈Mn if and only if there is a unitary matrix U ∈Mmn and a complex unit ξ such that φ(A⊗B) = ξU(φ1(...

We prove that for a right linear bounded normal operator on a quaternionic Hilbert space (quaternionic bounded normal operator) the norm and the numerical radius are equal. As a consequence of this result we give a new proof of the known fact that a non zero quaternionic compact normal operator has a non zero right eigenvalue. Using this we give a new proof of the spectral theorem for quaternio...