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A Measurable Selector in Kadison’s Carpenter’s Theorem
- Part of
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- Journal:
- Canadian Journal of Mathematics / Volume 72 / Issue 6 / December 2020
- Published online by Cambridge University Press:
- 16 July 2019, pp. 1505-1528
- Print publication:
- December 2020
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- Article
- Export citation
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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 in an earlier work. 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 
$\text{I}_{\infty }$ von Neumann algebras.
