q-numerical radius of rank-one operators and the generalized Buzano inequality

2025/03/06 by Denčić, Dušan, Stanković, Hranislav, Krstić, Mihailo +1
#47A07 #47A12 #47B99 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2503.05036

Abstract

Here, we study the q-numerical radius of rank-one operators on a Hilbert space H. More precisely, for q ∈ [0,1] and a, b ∈ H, we establish the formula ω_q(a ⊗ b) = (1)/(2)(‖a‖‖b‖ + q|⟨ a, b ⟩| + √(1-q²)√(‖a‖²‖b‖² - |⟨ a, b ⟩|²)), which represents a generalization of the well-known formula for the numerical radius of a rank-one operator in a Hilbert space, obtained by setting q = 1. As a corollary, we also derive a generalization of the classical Buzano inequality.

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