。
She owns a Turner painting.
Literal
She [topic-は] Turner [genitive-の] painting [object-を] [owns-所有している].
ターナー is J. M. W. Turner (1775–1851), the celebrated British Romantic landscape painter known for his luminous skies and atmospheric seascapes. His name renders into katakana as ターナー — straightforward phonetic mapping. Western artists are routinely transliterated this way in Japanese (ピカソ, ゴッホ, モネ). 所有する ('own, possess') is more formal than 持っている ('have'), implying legal or substantive ownership rather than just having something on hand. Used for property, art, businesses, intellectual rights. The polite-formal feel of 所有している matches the seriousness of owning a painting by a major artist.