Artie Shaw ( May 23 , 1910 -- December 30 , 2004 ) is considered to be one of the best jazz musicians of his time . He was a jazz clarinet player , composer , and bandleader . Arthur Jacob Arshawsky ( May 23 , 1910 -- December 30 , 2004 ) , better known as Artie Shaw , was an American jazz clarinetist , composer , and bandleader .