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arXiv · 2206.00986

The Banach algebras $AC(\sigma)$ and $BV(\sigma)$

Ian Doust·Michael Leinert·Alan Stoneham
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Abstract

The spaces $BV(\sigma)$ and $AC(\sigma)$ were introduced as part of a program to find a general theory which covers both well-bounded operators and trigonometrically well-bounded operators acting on a Banach space. Since their initial appearance it has become clear that the definitions could be simplified somewhat. In this paper we give a self-contained exposition of the main properties of these spaces using this simplified approach.

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Ian Doust, Michael Leinert, Alan Stoneham. 2022-06-02. The Banach algebras $AC(\sigma)$ and $BV(\sigma)$. https://doi.org/10.1007/s00025-022-01788-0

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