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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
199 views

$C(X)$-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 $H=\ell^2$ …
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29 votes
6 answers
9k views

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 …
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