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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Constructing non-AMNM weighted convolution algebras for every semilattice of infinite breadth
AU - Choi, Yemon
AU - Ghandehari, Mahya
AU - Pham, Hung Le
PY - 2025/2/1
Y1 - 2025/2/1
N2 - The AMNM property for commutative Banach algebras is a form of Ulam stability for multiplicative linear functionals. We show that on any semilattice of infinite breadth, one may construct a weight for which the resulting weighted convolution algebra fails to have the AMNM property. Our work is the culmination of a trilogy started in [Semigroup Forum 102 (2021), no. 1, 86-103] and continued in [European J. Combin. 94 (2021), article 103311]. In particular, we obtain a refinement of the main result of the second paper, by establishing a dichotomy for union-closed set systems that has a Ramsey-theoretic flavour.
AB - The AMNM property for commutative Banach algebras is a form of Ulam stability for multiplicative linear functionals. We show that on any semilattice of infinite breadth, one may construct a weight for which the resulting weighted convolution algebra fails to have the AMNM property. Our work is the culmination of a trilogy started in [Semigroup Forum 102 (2021), no. 1, 86-103] and continued in [European J. Combin. 94 (2021), article 103311]. In particular, we obtain a refinement of the main result of the second paper, by establishing a dichotomy for union-closed set systems that has a Ramsey-theoretic flavour.
KW - approximately multiplicative
KW - Semilattice
KW - set system
KW - Ulam stability
U2 - 10.1016/j.jfa.2024.110735
DO - 10.1016/j.jfa.2024.110735
M3 - Journal article
VL - 288
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 3
M1 - 110735
ER -