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

Functional Analysis 2

Note 1

Pre-Hilbert Space and Hilbert Space 

TANAKA Akio

[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^~₂ and H is contained in H^~₁ and H^~₂ as dense subspace of H, H^~₁ and H^~₂ are isomorphic by mapping what H transform H’s elements to itself .

[Explanation]

To be continued

Tokyo May 30, 2008

Sekinan Research Field of Language

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