Proper Improvement of Well-Known Numerical Radius Inequalities and Their Applications - Bhunia, Pintu; Paul, Kallol (Resultate der Mathematik, 2021)
New inequalities for the numerical radius of bounded linear operators defined on a complex Hilbert space H are given. In particular, it is established that if T is a bounded linear operator on a Hilbert space H then w 2 ( T ) ≤ min 0 ≤ α ≤ 1 α T ∗ T + ( 1 - α ) T T ∗ , where w ( T ) is the numerical radius of T . The inequalities obtained here are non-trivial improvement of the well-known numerical radius inequalities. As an application we estimate bounds for the zeros of a complex monic polynomial.