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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.
5
votes
1
answer
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$C(X)$-compact operators and families of compact operators
In this question Operators on Hilbert $C^*$-module and families of Fredholm operators I asked about the relation between being a family of compact operators $F:X \to K(H)$ on Hilbert space $H=\ell^2$ …
29
votes
6
answers
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Nonseparable Hilbert spaces
Being nonseparable Banach space is in fact nothing special: one meets the first
examples in the standard functional analysis course, when one learns about
$\ell^p$ or $L^p[0,1]$ spaces-these spaces ar …