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Isomorphisms of \(AC(\sigma )\) spaces for linear graphs

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Abstract

We show that among compact subsets of the plane which are drawings of linear graphs, two sets \(\sigma \) and \(\tau \) 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 \(C(\varOmega )\) spaces.

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Acknowledgements

The work of the first author was financially supported by the Ministry of Higher Education and Scientific Research of Iraq.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of New South Wales, UNSW, Sydney, 2052, Australia

    Shaymaa Al-shakarchi & Ian Doust

Authors
  1. Shaymaa Al-shakarchi
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  2. Ian Doust
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Correspondence to Ian Doust.

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Communicated by Jesus Araujo Gomez.

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Al-shakarchi, S., Doust, I. Isomorphisms of \(AC(\sigma )\) spaces for linear graphs. Adv. Oper. Theory 5, 474–488 (2020). https://doi.org/10.1007/s43036-020-00053-x

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  • DOI: https://doi.org/10.1007/s43036-020-00053-x

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