6
votes
Accepted
Bound in terms of harmonic oscillator
An easy way to see that this isn't working is as follows: Take $\psi=\psi_0=e^{-x^2/2}$ as the ground state of $H$, so $H\psi=\psi$. Since $\psi''=(x^2-1)\psi$ is not a multiple of $\psi_0$, we have $\...
4
votes
Accepted
Norm of a $2$-tuple of operators
$\newcommand\C{\Bbb C}\newcommand\om{\omega}$A counterexample is given by $E=\mathbb C^2$ and $K_1(x_1,x_2)=(x_1,0)$ and $K_2(x_1,x_2)=(0,x_2)$ for complex $x_1,x_2$.
Indeed, then $\om(K_1)=\om(K_2)=1=...
- 118k
3
votes
Accepted
Concentration of measure on spheres with respect to a unitary of trace approximately zero
This is indeed true. Assume WLOG that the matrices are diagonal. A useful way to handle the uniform measure on the sphere is that if you let $X_1,\ldots,X_n$ be iid (complex) Gaussians, then the ...
- 909
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