  The high-frequency transconductance and current noise of top-gated single
carbon nanotube transistors have been measured and used to investigate hot
electron effects in one-dimensional transistors. Results are in good agreement
with a theory of 1-dimensional nano-transistor. In particular the prediction of
a large transconductance correction to the Johnson-Nyquist thermal noise
formula is confirmed experimentally. Experiment shows that nanotube transistors
can be used as fast charge detectors for quantum coherent electronics with a
resolution of $13\mathrm{\mu e/\sqrt{Hz}}$ in the 0.2-$0.8 \mathrm{GHz}$ band.
