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Another identity relating to Hardy's inequality for ℓ2

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Article number25-70
<mark>Journal publication date</mark>31/12/2022
<mark>Journal</mark>Mathematical Inequalities and Applications
Issue number4
Number of pages3
Pages (from-to)1143-1145
Publication StatusPublished
<mark>Original language</mark>English


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∥.