Dilation theory offers various structural characterizations of numerical contractions, i. e. operators whose numerical radius does not exceed one. Among these, a recent factorization result establishes that a matrix A M₍ ₍ (C) is a numerical contraction if and only if it can be written as A = 2X*Y, where X, Y M₍ ₍ (C) satisfy X^*X + Y^*Y = Iₙ. In this article, we show how an equivalent formulation of this factorization may be employed to derive new bounds for the numerical radius. The principal contributions include generalizations of several known numerical radius inequalities for Hilbert space operators, thereby extending and refining existing results in operator theory.
Kumar et al. (Wed,) studied this question.