The quotient algebra of a finite von Neumann algebra
In: Pacific J. Math. 36, no. 3 (1971), 827-831; (1971)
Online
unknown
Zugriff:
We will prove the following: Let M be a finite von Neumann algebra with center Z and A a von Neumann subalgebra of Z. Let Ω be the spectrum space of A and identify A with C(Ω). Let e be a σ-weakly continuous linear map of M onto A such that e(x*x) = e(a%c*) ^ 0 for every xeM, e(ax) — ae(x) for every a e A and xeM, e(l) = 1 and e(x*x) Φ 0 for every nonzero xeM. For each ωeΩ, let mω denote the set of all xeM with e(x*x)(ω) = 0. Then mω is a closed ideal and the quotient C*-algebla M/xnω is a finite von Neumann algebra. Furthermore, if πω denote the canonical homomorphism of M onto Λf/m», then πω(N) is a von Neumann subalgebra of M/mω for every von Neumann subalgebra N containing A.
Titel: |
The quotient algebra of a finite von Neumann algebra
|
---|---|
Autor/in / Beteiligte Person: | Takesaki, Masamichi |
Link: | |
Quelle: | Pacific J. Math. 36, no. 3 (1971), 827-831; (1971) |
Veröffentlichung: | Pacific Journal of Mathematics, A Non-profit Corporation, 1971 |
Medientyp: | unknown |
Schlagwort: |
|
Sonstiges: |
|