Theorem / Eliashberg​, Tomita, Borchers / 27 February 2009

Theorem / Eliashberg​, Tomita, Borchers

Symplectic Language Theory 

TANAKA Akio 

Note 1 

Symplectic Topological Existence Theorem​

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​

[Theorem]​

(Eliashberg)​

Symplectic homeomorphism   is C0 convergent to differential 

homeomorphism .​

Under the upper condition, φ is symplectic homeomorphism.​

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[Note]​

1​

For language's understandability, differential homeomorphic C0 convergence is related with 

the finiteness and infinity of language. ​

2​

For the finiteness and infinity of language, next theorem is efficient to solve the problem.​

​

(Tomita's fundamental theorem)​

H       Hilbert space        ​

B(H)  Banach space B(H, H)​

N       B(H)'s *subalgebra that contains identity operator and closes for τuw topology​

J        Conjugate linear equidistance operator​

Δ       Unbounded positive self-adjoint operator​

Δit     τs-continuous 1 parameter unitary group​

(1) ​

(2) ​

​

(Borchers' theorem 1992)​

The theorem is deeply connected with Tomita's theorem.​

​

​

[Impression]​

Symplectic geometric structure is seemed to be solvable for language's
understandability that simultaneously connotes finiteness and infinity within. ​

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To be continued​

Tokyo February 27, 2009​

Sekinan Research Field of language​

Source:

  

    
                   https://writer.zoho.com/public/sekinan/SLTNote1SymplecticTopologicalExistenceTheorem1