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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