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The Banach Algebras \(AC(\sigma )\) and \(BV(\sigma )\)

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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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  1. In most later proofs we shall not explicitly consider this possibility. The diligent reader will check that that statements are typically trivially true for lists with just one element.

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Funding

The work of the third author was supported by the Research Training Program of the Department of Education and Training of the Australian Government.

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Authors and Affiliations

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

    Ian Doust & Alan Stoneham

  2. Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, Germany

    Michael Leinert

Authors
  1. Ian Doust
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  2. Michael Leinert
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  3. Alan Stoneham
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Contributions

An initial version of this work was prepared by the ID, ML. This was corrected and extended in collaboration with the AS. All authors have read and approved the final manuscript.

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Correspondence to Ian Doust.

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Doust, I., Leinert, M. & Stoneham, A. The Banach Algebras \(AC(\sigma )\) and \(BV(\sigma )\). Results Math 78, 20 (2023). https://doi.org/10.1007/s00025-022-01788-0

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