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Another identity relating to Hardy's inequality for ℓ2

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Another identity relating to Hardy's inequality for ℓ2. / Jameson, Graham.
In: Mathematical Inequalities and Applications, Vol. 25, No. 4, 25-70, 31.12.2022, p. 1143-1145.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Jameson, G 2022, 'Another identity relating to Hardy's inequality for ℓ2', Mathematical Inequalities and Applications, vol. 25, no. 4, 25-70, pp. 1143-1145. https://doi.org/10.7153/mia-2022-25-70

APA

Jameson, G. (2022). Another identity relating to Hardy's inequality for ℓ2. Mathematical Inequalities and Applications, 25(4), 1143-1145. Article 25-70. https://doi.org/10.7153/mia-2022-25-70

Vancouver

Jameson G. Another identity relating to Hardy's inequality for ℓ2. Mathematical Inequalities and Applications. 2022 Dec 31;25(4):1143-1145. 25-70. doi: 10.7153/mia-2022-25-70

Author

Jameson, Graham. / Another identity relating to Hardy's inequality for ℓ2. In: Mathematical Inequalities and Applications. 2022 ; Vol. 25, No. 4. pp. 1143-1145.

Bibtex

@article{e94bf0b58f62414c9f1e3ad7d8b1d52d,
title = "Another identity relating to Hardy's inequality for ℓ2",
abstract = "Let C denote the Ces{\`a}ro 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∥. ",
keywords = "Cesaro, Hardy, inequality",
author = "Graham Jameson",
year = "2022",
month = dec,
day = "31",
doi = "10.7153/mia-2022-25-70",
language = "English",
volume = "25",
pages = "1143--1145",
journal = "Mathematical Inequalities and Applications",
issn = "1331-4343",
publisher = "Element d.o.o.",
number = "4",

}

RIS

TY - JOUR

T1 - Another identity relating to Hardy's inequality for ℓ2

AU - Jameson, Graham

PY - 2022/12/31

Y1 - 2022/12/31

N2 - 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∥.

AB - 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∥.

KW - Cesaro

KW - Hardy

KW - inequality

U2 - 10.7153/mia-2022-25-70

DO - 10.7153/mia-2022-25-70

M3 - Journal article

VL - 25

SP - 1143

EP - 1145

JO - Mathematical Inequalities and Applications

JF - Mathematical Inequalities and Applications

SN - 1331-4343

IS - 4

M1 - 25-70

ER -