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Results tagged with oa.operator-algebras
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user 46855
Algebras of operators on Hilbert space, $C^*-$algebras, von Neumann algebras, non-commutative geometry
7
votes
Type III factor representation
A characterization of projection ortholattices of von Neumann algebras (and more generally JBW algebras) with no type I$_2$ component was given by Bunce and J.D.M. Wright in two papers: [1] and [2] (f …
- 2,213
6
votes
Which sigma-ideals in a sigma-algebra are ideals of null sets?
Your question has already been excellently answered from two points of view:
(a) looking at the quotient $\sigma$-algebra (measurable sets modulo null sets): when is it a measure algebra? [Joseph Va …
- 2,213
4
votes
Accepted
Literature on "real" $C^*$-algebras
Real operator algebras, Bing-Ren Li, Pub. Co. Pte. Ltd, 2003
(and the bibliography in that book).
Also the other operator algebra book by the same author has parts about real operator algebras (togeth …
- 2,213
2
votes
Projections in a W*-algebra as a continuous lattice?
The already given answer and comments have essentially solved the problem; however I
will show the way the question can be studied from the point of view of
"classical" lattice theory (say, the times …
- 2,213
1
vote
Can non-central projections still commute with all other projections?
[Below I consider only the unital case. I have to think about the non unital case, but it should be sufficient
to consider the associated $C^*$-algebra with unit $A\oplus K1$, with
$K$ the complex o r …
- 2,213
1
vote
Metrics and completions on the direct limit of matrices of all sizes over arbitrary fields
It seems that you might like the (normalized) rank metric, producing the first algebraic examples of continuous geometries and their coordinatizing rings. See the original papers of von Neumann (1936 …
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