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3 votes
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On compactly supported functions with prescribed sparse coordinates

This is a rather lazy version of an answer, but I will also indicate how I think a full answer can be produced. Let $u(x,z)$ be the solution of $-u''+qu=z u$ with $u(0,z)=0$, $u'(0,z)=1$. Then $$ B_L =...
Christian Remling's user avatar
4 votes
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Monotonicity of matrix conjugation

No, this is not true even if the matrices are $2 \times 2$ and $\alpha = 1/2$. For a concrete counter-example, consider $$A = \begin{bmatrix}1 & -\sqrt{3} \\ -\sqrt{3} & 3\end{bmatrix}, B = \...
Nathaniel Johnston's user avatar
3 votes

Monotonicity of matrix conjugation

This is a simple case of Furuta's inequality, see e.g. Theorem 1.1 of J IANGTAO Y UAN, FURUTA INEQUALITY AND q –HYPONORMAL OPERATORS Operators and Matrices Volume 4, Number 3 (2010), 405–415.
Derek's user avatar
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