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Abstract We sharpen the constant in the {\mathrm{KS}_{2}} Conjecture of Weaver [31] that was given by Marcus, Spielman and Srivastava [28] in their solution of the Kadison–Singer problem.We then apply this result to prove optimal asymptotic bounds on the size of partitions in the Feichtinger Conjecture.more » « less
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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 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.more » « less
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