This is the 4823rd most frequent Russian word.
известной
The Russian word "известной" means "famous" or "well-known" (feminine form, instrumental or dative case).
The word 'известной' is used as an adjective modifying 'Анна', indicating her 'famous' status derived from her achievements.
Анна стала известной благодаря своим художественным работам.
Anna became famous thanks to her artistic works.
Here, 'известной' is an adjective describing 'художницы' (artist), specifying her renown or fame.
Мы посетили выставку известной художницы.
We visited the exhibition of a famous artist.
The adjective 'известной' in conjunction with 'писательницы' (writer) denotes her recognition and established reputation.