polar decomposition in von Neumann algebras
As is a -algebra (http://planetmath.org/CAlgebra), it is known that belongs to . (proof will be added later)
Suppose . We intend to prove that commutes with .
For we have that
So and agree on .
Let . We have that and therefore
and so we can conclude that is identically zero in .
Clearly is also identically zero on .
Thus and agree on . Therefore and so
|Title||polar decomposition in von Neumann algebras|
|Date of creation||2013-03-22 17:28:54|
|Last modified on||2013-03-22 17:28:54|
|Last modified by||asteroid (17536)|