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**Translation-finite sets and weakly compact derivations from $\ell^1(\mathbb Z_+)$ to its dual.** / Choi, Yemon; Heath, Matthew J.

Research output: Contribution to journal › Journal article › peer-review

Choi, Y & Heath, MJ 2010, 'Translation-finite sets and weakly compact derivations from $\ell^1(\mathbb Z_+)$ to its dual', *Bulletin of the London Mathematical Society*, vol. 42, no. 3, pp. 429-440. https://doi.org/10.1112/blms/bdq003

Choi, Y., & Heath, M. J. (2010). Translation-finite sets and weakly compact derivations from $\ell^1(\mathbb Z_+)$ to its dual. *Bulletin of the London Mathematical Society*, *42*(3), 429-440. https://doi.org/10.1112/blms/bdq003

Choi Y, Heath MJ. Translation-finite sets and weakly compact derivations from $\ell^1(\mathbb Z_+)$ to its dual. Bulletin of the London Mathematical Society. 2010;42(3):429-440. https://doi.org/10.1112/blms/bdq003

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title = "Translation-finite sets and weakly compact derivations from $\ell^1(\mathbb Z_+)$ to its dual",

abstract = "We characterize those derivations from the convolution algebra ℓ1(ℤ+) to its dual that are weakly compact, providing explicit examples that are not compact. The characterization is combinatorial, in terms of {\textquoteleft}translation-finite{\textquoteright} subsets of ℤ+, and we investigate how this notion relates to other notions of {\textquoteleft}smallness{\textquoteright} for infinite subsets of ℤ+. In particular, we prove that a set of strictly positive Banach density cannot be translation-finite; the proof has a Ramsey-theoretic flavour.",

author = "Yemon Choi and Heath, {Matthew J.}",

year = "2010",

doi = "10.1112/blms/bdq003",

language = "English",

volume = "42",

pages = "429--440",

journal = "Bulletin of the London Mathematical Society",

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publisher = "Oxford University Press",

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T1 - Translation-finite sets and weakly compact derivations from $\ell^1(\mathbb Z_+)$ to its dual

AU - Choi, Yemon

AU - Heath, Matthew J.

PY - 2010

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N2 - We characterize those derivations from the convolution algebra ℓ1(ℤ+) to its dual that are weakly compact, providing explicit examples that are not compact. The characterization is combinatorial, in terms of ‘translation-finite’ subsets of ℤ+, and we investigate how this notion relates to other notions of ‘smallness’ for infinite subsets of ℤ+. In particular, we prove that a set of strictly positive Banach density cannot be translation-finite; the proof has a Ramsey-theoretic flavour.

AB - We characterize those derivations from the convolution algebra ℓ1(ℤ+) to its dual that are weakly compact, providing explicit examples that are not compact. The characterization is combinatorial, in terms of ‘translation-finite’ subsets of ℤ+, and we investigate how this notion relates to other notions of ‘smallness’ for infinite subsets of ℤ+. In particular, we prove that a set of strictly positive Banach density cannot be translation-finite; the proof has a Ramsey-theoretic flavour.

U2 - 10.1112/blms/bdq003

DO - 10.1112/blms/bdq003

M3 - Journal article

VL - 42

SP - 429

EP - 440

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

IS - 3

ER -