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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=...
Iosif Pinelis's user avatar
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 ...
Marcus M's user avatar
  • 909
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 $\...
Christian Remling's user avatar
1 vote

Minimal norm problem with linear combination of translation operator to be estimated

I think, fundamentally, you are trying to make the question a lot more complicated than it really is and your approach is doomed to fail. Here are some problems. You cannot expect to use "linear ...
Willie Wong's user avatar
  • 37.6k
3 votes

Minimal norm problem whose unknown is an operator

Let me try to explain the series of comments by David Gao and transform it into a complete answer. It is worth keeping in mind the types of objects here: The elements $x, y$ are considered to be ...
Willie Wong's user avatar
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