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]]>Thanks so much and keep up the awesome work!

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]]>Also, there’s a nice perturbation approach to the spectral theorem (due to von Neumann-Wigner; see http://www.math.harvard.edu/~knill/teaching/math19b_2011/handouts/lecture35.pdf).

For the operator version, need to look at more carefully, but see https://terrytao.wordpress.com/2011/12/20/the-spectral-theorem-and-its-converses-for-unbounded-symmetric-operators/

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]]>Furthermore, we easily see and (since fixes by definition) . So .

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]]>Could you give some details of what ur day consisted of for math before you became highly pro (during 2012 maybe).

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