Home > Research > Publications & Outputs > Translation-finite sets and weakly compact deri...

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

Research output: Contribution to journalJournal articlepeer-review

Published

### Standard

In: Bulletin of the London Mathematical Society, Vol. 42, No. 3, 2010, p. 429-440.

Research output: Contribution to journalJournal articlepeer-review

### Harvard

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

### Author

Choi, Yemon ; Heath, Matthew J. / Translation-finite sets and weakly compact derivations from $\ell^1(\mathbb Z_+)$ to its dual. In: Bulletin of the London Mathematical Society. 2010 ; Vol. 42, No. 3. pp. 429-440.

### Bibtex

@article{9a44a5fb0e44452fb58f53f7a578dcff,
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",
issn = "0024-6093",
publisher = "Oxford University Press",
number = "3",

}

### RIS

TY - JOUR

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

Y1 - 2010

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 -