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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

2 votes

why is this a sufficient condition for a domain to be a core of an unbounded operator?

See also Theorem VIII.11 in Reed-Simon (p.269 vol. 1).
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1 vote

Duality relations for Lebesgue spaces of sections of vector bundles

The existence of a finite trivialising cover is a less stringent condition than one would expect: see Does every vector bundle allow a finite trivialization cover? (Sorry for the commentlike answer b …
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1 vote

Are there examples of compact infinite dimensional manifolds?

Yes. Compact Hilbert cube manifolds, for instance.
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