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.
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Sever S. Dragomir, Inequalities for Some Functionals Associated with Bounded Linear Operators in Hilbert Spaces. Publ. Res. Inst. Math. Sci. 43 (2007), no. 4, pp. 1095–1110DOI 10.2977/PRIMS/1201012380