A non-smooth continuous unitary representation of a Banach-Lie group

Daniel Beltita, Karl-Hermann Neeb

In this note we show that the representation of the additive group of the Hilbert space $L^2([0,1],\mathbb{R})$ on $L^2([0,1],\C)$ given by the multiplication operators $\pi (f):=e^{if}$ is…