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A C*-algebra is a complex Banach algebra together with an isometric antilinear involution satisfying (a b)* = b* a* and the C*-identity ‖a* a‖ = ‖a‖². Related tags: [banach-algebras], [von-neumann-algebras], [operator-algebras], [spectral-theory].

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 …
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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 …
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