Another identity relating to Hardy's inequality for ℓ2

Jameson, Graham (2022) Another identity relating to Hardy's inequality for ℓ2. Mathematical Inequalities and Applications, 25 (4): 25-70. pp. 1143-1145. ISSN 1331-4343

Abstract

Let C denote the Cesàro operator on ℓ2, I the identity and ∥x∥ the ℓ -norm of x. Complementing an earlier result, an exact expression is derived for ∥(C − I)x∥2 . Implications include the inequalities 1/√2 ∥x∥ ≼ ∥(C − I)x∥ ≼ ∥x∥ and ∥(C − I)x∥ ≽ ∥CT − I)x∥.