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A Hilbert space $H$ is a real or complex vector space endowed with an inner product such that $H$ is a complete metric space when endowed with the norm induced by this inner product.

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Self-adjoint bounded operator, resolution of the identity, def. of the diagonal

Let $A$ be a self adjoint bounded linear operator with a continuous spectrum $\sigma(A)=[a,b]$ which acts on a separable Hilbert space. Let $E_\lambda$ be its resolution of the identity. For exampl …
Yakov Dymarskii's user avatar