Tuesday 23 July 2013

Symplectic Topological Existence Theorem​ From Eliashberg to Tomita and Borcher

sekinanlogoshome
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(HH)
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

To be continued
Tokyo February 27, 2009
Sekinan Research Field of language
 

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