Geodesic
A Measurable Selector in Kadison’s Carpenter’s Theorem
Canadian journal of mathematics, Tome 72 (2020) no. 6, pp. 1505-1528

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DOI

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.
DOI : 10.4153/S0008414X19000373
Mots-clés : Schur–Horn problem, diagonal of self-adjoint operator, Carpenter’s theorem 
Bownik, Marcin; Szyszkowski, Marcin. A Measurable Selector in Kadison’s Carpenter’s Theorem. Canadian journal of mathematics, Tome 72 (2020) no. 6, pp. 1505-1528. doi: 10.4153/S0008414X19000373
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     title = {A {Measurable} {Selector} in {Kadison{\textquoteright}s} {Carpenter{\textquoteright}s} {Theorem}},
     journal = {Canadian journal of mathematics},
     pages = {1505--1528},
     year = {2020},
     volume = {72},
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     doi = {10.4153/S0008414X19000373},
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