Inequalities for Some Functionals Associated with Bounded Linear Operators in Hilbert Spaces

Abstract

Some inequalities between the operator norm, numerical radius and the functionals vp, δp defined in terms of the real and imaginary part of ‹Ax, x›, x ∈ H, ‖x‖ = 1 are established. New upper bounds for the nonnegative quantity ‖A‖2 − w2 (A) with A ∈ B(H) that complement some recent results of the author are given as well.