Symplectic Topological Existence Theorem​ From Eliashberg to Tomita and Borcher

sekinanlogoshome​

Symplectic Language Theory 

TANAKA Akio     

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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 eficient to solve the problem.​

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(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) ​

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(Borchers' theorem 1992)​

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

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[Impression]​

Symplectic geometric structure is seemed to be solvable for language's understandability that 

simultaneously connotes finiteness and infinity within. ​

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[References]​

<Topological approach>​

#1 Topological Approach​

<Language's understandability>​

#2 Deep Fissure between Word and Sentence​

#3 Finiteness in Infinity on Language​

<Related theorems>​

#4 Tomita's Fundamental Theorem​

#5 Borchers' Theorem​

To be continued​​

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Tokyo February 27, 2009​

Sekinan Research Field of language​
 

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