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arXiv · 0708.2366

A Note On The Kadison-Singer Problem

Charles A. Akemann·Betul Tanbay·Ali Ulger
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Abstract

Let H be a separable Hilbert space with a fixed orthonormal basis (e_n), n>=1, and B(H) be the full von Neumann algebra of the bounded linear operators T: H -> H. Identifying l^\infty = C(βN) with the diagonal operators, we consider C(βN) as a subalgebra of B(H). For each t in βN, let [δ_t] be the set of the states of B(H) that extend the Dirac measure δ_t. Our main result shows that, for each t in βN, this set either lies in a finite dimensional subspace of B(H)* or else it must contain a homeomorphic copy of βN.

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Charles A. Akemann, Betul Tanbay, Ali Ulger. 2007-08-17. A Note On The Kadison-Singer Problem. https://arxiv.org/abs/0708.2366

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