Abstract
Abstract In analysing an L2-space we can profitably exploit the interplay of its inner product structure with the convergence notions associated with its norm. An inner product space X is called a Hilbert space if the associated norm makes X a Banach space (that is, Cauchy sequences in X converge). Theorem 28.16 tells us that L2 is a Hilbert space, as is L2 (I) for any interval I.
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