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The Banach Space C(K)

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Banach Spaces of Continuous Functions as Dual Spaces

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Abstract

The main aim of this chapter is to determine when a space of the form C(K) for a compact space K is a dual space or a bidual space,either isometrically or isomorphically. However, we shall first discuss when two spaces C(K) and C(L) are isomorphic and when they are isometrically isomorphic. Some results come from rather elementary considerations, but some require more sophisticated background.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Lancaster, Lancaster, UK

    H. G. Dales

  2. Center of Excellence in Computation Algebra, and Topology (CECAT), Chapman University, Orange, CA, USA

    F. K. Dashiell Jr.

  3. Department of Mathematical Sciences, University of Alberta, Edmonton, AB, Canada

    A. T.-M. Lau

  4. Department of Pure Mathematics, University of Leeds, Leeds, UK

    D. Strauss

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  1. H. G. Dales
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Dales, H.G., Dashiell, F.K., Lau, A.TM., Strauss, D. (2016). The Banach Space C(K). In: Banach Spaces of Continuous Functions as Dual Spaces. CMS Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-32349-7_6

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