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arXiv · 1803.03632

Measurable selector in Kadison's carpenter's theorem

Marcin Bownik·Marcin Szyszkowski
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Abstract

We show the existence of a measurable selector in Carpenter's Theorem due to Kadison. This solves a problem posed by Jasper and the first author. As an application we obtain a characterization of all possible spectral functions of shift-invariant subspaces of $L^2(\mathbb R^d)$ and Carpenter's Theorem for type I$_\infty$ von Neumann algebras.

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Marcin Bownik, Marcin Szyszkowski. 2018-03-09. Measurable selector in Kadison's carpenter's theorem. https://arxiv.org/abs/1803.03632

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