Constructing non-AMNM weighted convolution algebras for every semilattice of infinite breadth
Abstract
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.
Keywords
Cite
@article{arxiv.2305.18272,
title = {Constructing non-AMNM weighted convolution algebras for every semilattice of infinite breadth},
author = {Yemon Choi and Mahya Ghandehari and Hung Le Pham},
journal= {arXiv preprint arXiv:2305.18272},
year = {2024}
}
Comments
v1: AMS-LaTeX, 17 pages, 2 figures. Submitted for publication. arXiv admin note: substantial text overlap with arXiv:1702.06266, arXiv:1901.00082. v2: Minor revisions in Section 1. Accepted for publication in J. Funct. Anal