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In page Family of Vladimir the Great:

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Anna (March 13, 963 - 1011/12) was the daughter of Byzantine Emperor Romanos II (r. 959–963)) and the Empress Theophano. She was also the sister of Emperors Basil II Bulgaroktonos (the Bulgar-Slayer; r. 976–1025) and Constantine VIII. Anna was a Porphyrogenita, a legitimate daughter born in the special purple chamber of the Byzantine Emperor's Palace. Anna's hand was considered by Vladimir such a prize that he allegedly became Christian (988) just to marry her.[citation needed]