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

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... table 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> → | F=2, m_F=0> in a sodium Bose-Einstein condensate and determined a density-dependent frequency shift of (2.44± 0.25) × 10^-12 Hz cm^3.