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

www.sekinan.org