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What is a central projection in the context of a C*-algebra or a W*-algebra? Unfortunately while I see results on this concept, I haven't been able to find a definition.

Thanks!

1 Answers 1

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It is just a projection that is central (i.e., in the center). That is, a central projection in a *-algebra $A$ is an element $p\in A$ such that $p=p^*$, $p^2=p$, and $px=xp$ for all $x\in A$.

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    Ah! Thanks so much. I thought there was a deeper meaning to it due to the definition in geometry. – 2017-01-14
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    That a definition seems simple doesn't tell that it has no "deeper meaning". In fact central projections are pretty interesting and important objects in von Neumann algebras and are in particular very important when it comes to classification/decomposition of vNAs. – 2017-01-26