Abstract
In this chapter, we consider subsets of the function spaces introduced in Chapter 3. Two fundamental properties of these subsets are convexity and compactness, which in applications are important. We first consider convex subsets (see 4.1–4.4), and in particular we prove the projection theorem in Hilbert spaces.
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© 2016 Springer-Verlag London
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Alt, H.W. (2016). Subsets of function spaces. In: Linear Functional Analysis. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-7280-2_4
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DOI: https://doi.org/10.1007/978-1-4471-7280-2_4
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Publisher Name: Springer, London
Print ISBN: 978-1-4471-7279-6
Online ISBN: 978-1-4471-7280-2
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