Isomorphisms of $AC(\sigma)$ spaces for linear graphs
Functional Analysis
2021-05-31 v2
Abstract
We show that among compact subsets of the plane which are drawings of linear graphs, two sets and are homeomorphic if and only if the corresponding spaces of absolutely continuous functions (in the sense of Ashton and Doust) are isomorphic as Banach algebras. This gives an analogue for this class of sets to the well-known result of Gelfand and Kolmogorov for spaces.
Cite
@article{arxiv.1810.08288,
title = {Isomorphisms of $AC(\sigma)$ spaces for linear graphs},
author = {Shaymaa Al-shakarchi and Ian Doust},
journal= {arXiv preprint arXiv:1810.08288},
year = {2021}
}
Comments
18 pages. Minor revisions. To appear in Adv. Oper, Theory