Saturday, 28 April 2018

Functional Analysis 2 Note 1 Pre-Hilbert Space and Hilbert Space


Note 1

Pre-Hilbert Space and Hilbert Space 


[Theorem]
For pre-Hilbert space H, there exists Hilbert space H~ that contains pre-Hilbert space H as dense subspace .
When there exist two Hilbert spaces H~1 and H~and H is contained in H~1 and H~as dense subspace of H, H~1 and H~are isomorphic by mapping what H transform H’s elements to itself .

[Explanation]


To be continued
Tokyo May 30, 2008

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