The aim of this paper is to provide new upper bounds ω(T), which denotes the numerical radius a bounded operator T on Hilbert space (H,⟨·,·⟩). We show Aczél inequality in terms |T|. Next, we give certain inequalities about A-numerical ωA(T) and A-operator seminorm ∥T∥A an T. also present several results related 2×2 block matrices semi-Hilbert operators, by using symmetric matrices.

Let S be any bounded linear operator defined on a complex Hilbert space id="M2"> H . In this paper, we present some numerical radius inequalities involving the generalized Aluthge transform to attain upper bounds for radius. Numerical computations are carried out particular cases of...

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

Abstract. We study a factorization of bounded linear maps from an operator space A to its dual space A∗. It is shown that T : A −→ A∗ factors through a pair of a column Hilbert spaces Hc and its dual space if and only if T is a bounded linear form on A ⊗ A by the canonical identification equipped with a numerical radius type Haagerup norm. As a consequence, we characterize a bounded linear map ...

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...

We show that a bounded linear operator A ∈ B(H) is a multiple of a unitary operator if and only if AZ and ZA always have the same numerical radius or the same numerical range for all (rank one) Z ∈ B(H). More generally, for any bounded linear operators A,B ∈ B(H), we show that AZ and ZB always have the same numerical radius (resp., the same numerical range) for all (rank one) Z ∈ B(H) if and on...

We observe that the classical notion of numerical radius gives rise to a smoothness in space bounded linear operators on certain Banach spaces, whenever is norm. characterize Birkhoff-James orthogonality finite-dimensional space, endowed with Some examples are also discussed illustrate geometric differences between norm and usual operator norm, from viewpoint smoothness.

Let X be a Banach space with the Radon-Nikodỳm property. Then, the following are equivalent. (i) X has numerical index 1. (ii) |x∗∗(x∗)| = 1 for all x∗ ∈ ex(BX∗ ) and x∗∗ ∈ ex(BX∗∗ ). (iii) X is an almost-CL-space. (iv) There are a compact Hausdorff space K and a linear isometry J : X → C(K) such that |x∗∗(J∗δs)| = 1 for all s ∈ K and x∗∗ ∈ ex(BX∗∗ ). If X is a real space, the above conditions ...