  We have investigated the properties of Bose-Einstein condensates of sodium
atoms in the upper hyperfine ground state in a purely optical trap. Condensates
in the high-field seeking $| F=2, m_F=-2>$ state were created from initially
prepared $| F=1,m_F=-1>$ condensates using a one-photon microwave transition at
1.77 GHz. The condensates were stored in a large-volume optical trap created by
a single laser beam with an elliptical focus. We found condensates in the
stretched state $| F=2, m_F=-2>$ to be stable for several seconds at densities
in the range of $10^{14}$ atoms/cm$^{3}$. In addition, we studied the clock
transition $| F=1, m_F=0>$ $\to$ $| F=2, m_F=0>$ in a sodium Bose-Einstein
condensate and determined a density-dependent frequency shift of $(2.44\pm
0.25) \times 10^{-12}$ Hz cm$^{3}$.
