Muon Spin Relaxation and Susceptibility Studies of the Pure and Diluted Spin $\frac{1}{2}$ Kagomé-Like Lattice System $({\mathrm{C}\mathrm{u}}_x{\mathrm{Z}\mathrm{n}}_{1-x}{)}_3{\mathrm{V}}_{\mathrm{2}}{\mathrm{O}}_7\mathrm{(}\mathrm{O}{\mathrm{H}}_{\mathrm{2}}\mathrm{)}$ $2{\mathrm{H}}_2\mathrm{O}$

Muon spin relaxation and magnetic susceptibility measurements have been performed on the pure and diluted spin $\frac{1}{2}$ kagomé system $({\mathrm{C}\mathrm{u}}_x{\mathrm{Z}\mathrm{n}}_{1-x}{)}_3{\mathrm{V}}_2{\mathrm{O}}_7(\mathrm{O}\mathrm{H}{)}_2$ $2{\mathrm{H}}_{\mathrm{2}}\mathrm{O}$. In the pure $x=1$ system we found a slowing down of Cu spin fluctuations with decreasing temperature towards $T\sim 1\mathrm{K}$, followed by slow and nearly temperature-independent spin fluctuations persisting down to $T=50\mathrm{m}\mathrm{K}$, indicative of quantum fluctuations. No indication of static spin freezing was detected in either of the pure ($x=1.0$) or diluted samples. The observed magnitude of fluctuating fields indicates that the slow spin fluctuations represent an intrinsic property of kagomé network rather than impurity spins.