Abstract
A Hilbert space H is a vector space endowed with an inner product such that the norm associated with the inner product is complete. We use the notation 〈 , 〉 for the inner product, and \(\Vert \,f\Vert = \sqrt{\langle \,f, f\rangle }\) for the norm.
The study of various topologies and the relations among them is, despite its current popularity in the theory of topological linear spaces, a pretty dull business.
P.R. Halmos (1916–2006)
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Coudène, Y. (2016). Weak Convergence. In: Ergodic Theory and Dynamical Systems. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-7287-1_16
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DOI: https://doi.org/10.1007/978-1-4471-7287-1_16
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