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arXiv · 1710.09073

Isomorphisms of $AC(\sigma)$ spaces for countable sets

Ian Doust·Shaymaa Al-shakarchi
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Abstract

It is known that the classical Banach--Stone theorem does not extend to the class of $AC(\sigma)$ spaces of absolutely continuous functions defined on compact subsets of the complex plane. On the other hand, if $\sigma$ is restricted to the set of compact polygons, then all the corresponding $AC(\sigma)$ spaces are isomorphic. In this paper we examine the case where $\sigma$ is the spectrum of a compact operator, and show that in this case one can obtain an infinite family of homeomorphic sets for which the corresponding function spaces are not isomorphic.

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Ian Doust, Shaymaa Al-shakarchi. 2017-10-25. Isomorphisms of $AC(\sigma)$ spaces for countable sets. https://doi.org/10.1007/978-3-319-75996-8_11

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