Abstract
We start with the classification of all examples of algebras with the Kadison-Singer property. In this chapter, we determine, for a fixed Hilbert space H, which subalgebras \(A\subseteq B(H)\) can possibly have the Kadison-Singer property. For this, we introduce the notion of maximal abelian subalgebras and discuss its properties. Next, we show that only maximal abelian subalgebras can possibly have the Kadison-Singer property. Subsequently, we give three main examples of maximal abelian subalgebras, which play a key role in the final classification.
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Stevens, M. (2016). Maximal Abelian C\(^*\)-Subalgebras. In: The Kadison-Singer Property. SpringerBriefs in Mathematical Physics, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-47702-2_4
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DOI: https://doi.org/10.1007/978-3-319-47702-2_4
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-47701-5
Online ISBN: 978-3-319-47702-2
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