Several refinements of norm and numerical radius inequalities bounded linear operators on a complex Hilbert space are given. In particular, we show that if A is operator space, then 14A*A+AA*≤18A+A*2+A−A*2+c2(A+A*)+c2(A−A*)≤w2(A) 12A∗A+AA∗−14(A+A∗)2(A−A∗)212≤w2(A)≤12A∗A+AA∗, where ∥⋅∥, w(⋅) c(⋅) the norm, Crawford number, respectively. Further, prove A, D AD∗≤∫01(1−t)(A2+D2)/2+tAD∗I2dt12≤12A2+D...

Let A be a bounded linear positive operator on complex Hilbert space \({\mathcal {H}}.\) Furthermore, let {B}}_A\mathcal {(H)}\) denote the set of all operators {H}}\) whose A-adjoint exists, and \({\mathbb {A}}\) signify diagonal matrix with entries are A. Very recently, several {A}}\)-numerical radius inequalities \(2\times 2\) matrices were established. In this paper, we prove few new for \(...

The main goal of this article is to present new inequalities for the recently defined generalized numerical radius block operators.

In this paper we find new estimate for the numerical radius of a given matrix, and we prove that, this estimate is better than any estimate for the numerical radius. We present also new bounds for the zero of polynomials by using new estimate for the numerical radius of a companion matrix of a given polynomial and matrix inequalities.

The publication of new tables of calibration of some fundamental parameters of Galactic B0-B5 supergiants in the two classes Ia and Ib allows to particularize the eight parameters conjecture that model five fundamental parameters. The numerical expressions for visual magnitude, radius, mass, luminosity and surface gravity are derived for supergiants in the range of temperature between 29700 K a...