On the p-numerical radii of Hilbert space operators.

In this paper, we give new results for the p-numerical radii w p ⋅ of Hilbert space operators. It is shown, among other inequalities, that if A is a Hilbert space operator, which belongs to the Schatten p-class, then w p p (A) ≥ w p / 2 p / 2 (A 2) 2 p / 2 + A ∗ A + A A ∗ p / 2 p / 2 2 p + inf θ ∈ R Re ⁡ (e i θ A) p p − Im ⁡ (e i θ A) p p 2 and w p p (A) ≤ 2 p / 2 − 2 inf θ ∈ R Re ⁡ ((e i θ A) 2) p / 2 p / 2 + A ∗ A + A A ∗ p / 2 p / 2 4 for 4 ≤ p < ∞. Also, w p p (A) ≥ w p / 2 p / 2 A 2 4 + A ∗ A + A A ∗ p / 2 p / 2 2 p / 2 + 2 + inf θ ∈ R Re ⁡ (e i θ A) p p − Im ⁡ (e i θ A) p p 2 and w p p (A) ≤ inf θ ∈ R Re ⁡ ((e i θ A) 2) p / 2 p / 2 + A ∗ A + A A ∗ p / 2 p / 2 2 p / 2 for 2 ≤ p ≤ 4 , where ⋅ p is the Schatten p-norm. Applications of these inequalities to certain classes of operators are also given. [ABSTRACT FROM AUTHOR]