On Numerical Radius Bounds Involving Generalized Aluthge Transform

Abstract

In this paper, we establish some upper bounds of the numerical radius of a bounded linear operator S defined on a complex Hilbert space with polar decomposition S = U ∣ S ∣ , involving generalized Aluthge transform. These bounds generalize some bounds of the numerical radius existing in the literature. Moreover, we consider particular cases of generalized Aluthge transform and give some examples where some upper bounds of numerical radius are computed and analyzed for certain operators.

On Some Numerical Radius Inequalities Involving Generalized Aluthge Transform

“…see [18]. Inequality (41) obtained in Theorem 14 gives better bounds of numerical radius of S for different choices of f and g in (10) when…”

Spectral Radius Formulas Involving Generalized Aluthge Transform

“…Clearly, Hermitian operators are self-adjoint and hence symmetric operators. The symmetric operators involved in Cartesian decomposition are helpful to develop the spectral radius for-mulas and numerical radius inequalities involving Aluthge transform [10][11][12].…”