Re: Toa'n tu+? De Rham Re: Gelfand-Kolmogorov, Najmark & Stone Re: Gelfand-Naimark

[Aiviet Nguyen <aiviet2@yahoo.com>]

Hi,

--- Phung Ho Hai <phung@msri.org> wrote:
> >    Ho^m qua to^i  nha('c to+'i toa'n tu+? De Rham
> la`
> > vi` cu`ng mo^.t dda.i so^' ne^'u to^i define hai
> toa'n
> > tu+? De Rham kha'c nhau to^i se~ construct
> ddu+o+.c
> > hai geometry kha'c nhau.  ( Connes go.i toa'n tu+?
> > na`y la` toa'n tu+? Dirac). Ddie^?m na`y to^i
> tha^'y
> > nhie^`u ngu+o+`i nha^`m khi vie^'t ve^`
> > Gelfand-Naimark theorem. Ho. hay tu+o+ng mo^.t
> ca^u
> > kie^?u :" Dda.i so^' ca'c  toa'n tu+? (hoa(.c
> ha`m) 
> > hoa`n toa`n tu+o+ng ddu+o+ng vo+'i  geometry" Tu+`
>                                       ^^^^^^^^
> Trong di.nh ly' Gelfand-Najmark kho^ng co' toa'n
> tu+? DeRham na`o ca? vi`
> chi? xe't o+? level topo. Ba'c nha^`m vo+'i geometry
> (differential
> geometry) co' le~ lu'c do' mo+'i ca^`n de^'n toa'n
> tu+? DeRham-

  Chuye^.n ddo' ra^'t co' the^?. Tuy nhie^n Connes va`
ca'c NCGeometrists hay refer to+'i Naimark-Gelfand
trong mo^.t specific context o+? geometry level va`
la`m mo^.t so^' ngu+o+`i bi. confused. Ddo' ch'nh la`
starting point cu?a NCG. Ne^'u no'i ro~ ra`ng va`
ta'ch ba.ch algebra ~ topo, DeRham ~ geometry thi` OK.
Nhu+ng ho. hay no'i mo^.t ca^u xanh ro+`n:
non-commutative algebra of operators replaces
commutative geometry.

  Trong cuo^'n NCG,Connes refer to+'i Naimark-Gelfand
ba`i na(m 1943:
"On the embedding of normed rings into the ring of
operators in Hilber space Mat. sb. t12 (1943) 197"
va` mo^.t ba`i kha'c tre^~ ho+n va`o na(m 1948.

Cheers
Aiviet
Cheers
Aiviet


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