very respected / very well known
Someone having good reputation
reputation – 評判，声価，うわさ，定評
Amitabh Bachaaan is looked upon as the most prestigious, actor in the Bollywood.
Barack Obama is very prestigious because he is the president of USA. He also went to a very prestigious university.
Mary studied at Cambridge, a very prestigious university in the world.
木蘭の涙 / スターダストレビュー （ピアノ＆バイオリン）