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4 exercise(s) shown, 0 hidden
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Find a simple proof for the von Neumann bicommutant theorem, in finite dimensions.
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Again in finite dimensions, [math]H=\mathbb C^N[/math], compute explicitly the von Neumann algebra [math] \lt T \gt \subset B(H)[/math] generated by a single operator.
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Try understanding what the law of the simplest non-normal operator,
[[math]]
J=\begin{pmatrix}0&1\\0&0\end{pmatrix}
[[/math]]
acting on [math]H=\mathbb C^2[/math] should be. Look also at more general Jordan blocks.
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Develop a full theory of finite quantum spaces, by enlarging what has been said above, with various geometric topics, of your choice.