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Hilbert Spaces

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Part of the Graduate Texts in Mathematics book series (GTM,volume 282)

Abstract

In this chapter, we will see a clean description of the bounded linear functionals on a Hilbert space. We will also see that every Hilbert space has an orthonormal basis, which make Hilbert spaces look much like standard Euclidean spaces but with infinite sums replacing finite sums.

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© 2020 Sheldon Axler

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Axler, S. (2020). Hilbert Spaces. In: Measure, Integration & Real Analysis. Graduate Texts in Mathematics, vol 282. Springer, Cham. https://doi.org/10.1007/978-3-030-33143-6_8

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