Symplectic Language Theory Note 1 Symplectic Topological Existence Theorem

Symplectic Language Theory

TANAKA Akio

   

Note 1

Symplectic Topological Existence Theorem


[Theorem]
(Eliashberg)
Symplectic homeomorphism  
 is C0 convergent to differential homeomorphism .
Under the upper condition, φ is symplectic homeomorphism.


[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.

(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. 


[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

<Related twitter site>
#6

sekinanlu

To be continued
Tokyo February 27, 2009

Sekinan Research Field of language

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