Abu-Omar and Kittaneh [Numerical radius inequalities for products of Hilbert space operators, J. Operator Theory 72(2) (2014), 521-527], wonder what is the smallest constant c such thatw(AB) ? c||A||w(B) all bounded linear operators A, B on a complex with A positive. Here, w(?) stands numerical radius. In this paper, we prove that = 3?3/4.

Operator radii wp(T) for a bounded linear operator T on a Hubert space were introduced in connection with unitary p-dilations. We shall be concerned with universal estimates for the ratios wp(ST)/(wa(S)wl,(T)) for commuting operators S, T and o, p > 0. 1. All operators in this paper are bounded linear operators on a complex Hubert space §. We say an operator T belongs to the class G (0 < p < oo...

New inequalities for the A-numerical radius of products and sums operators acting on a semi-Hilbert space, i.e. space generated by positive semidefinite operator A, are established. In particular, every T S which admit A-adjoints, it is proved that ?A(TS) ? 1/2?A(ST) + 1/4 (||T||A||S||A ||TS||A), where ?A(T) ||T||A denote A-operator seminorm an respectively.

In this work, an improvement of Hölder–McCarty inequality is established. Based on that, several refinements the generalized mixed Schwarz are obtained. Consequently, some new numerical radius inequalities proved. New for $$n\times n$$ matrix Hilbert space operators proved as well. Some earlier results were in literature also given. presented refined and it shown to be better than literature.

Abstract In this paper, we improve some numerical radius inequalities for Hilbert space operators under suitable condition. We also compare our results with known results. As application of result, obtain an operator inequality.

The numerical range W (A) of a bounded linear operator A on a Hilbert space is the collection of complex numbers of the form (Av, v) with v ranging over the unit vectors in the Hilbert space. In terms of the location of W (A), inclusion regions are obtained for W (Ak) for positive integers k, and also for negative integers k if A−1 exists. Related inequalities on the numerical radius w(A) = sup...