The author of a terrific Irving Berlin biography (As Thousands Cheer), Laurence Bergreen produces a similarly astute character analysis of the renowned trumpet player, too often viewed as a musical genius but an Uncle Tom in race relations. On the contrary, Bergreen shows, Louis Armstrong (1901-71) was that rarest of human beings, someone who could respond to injustice with a determination to overcome that never included bitterness. Slightly stronger on milieu than music, Bergreen conveys such zest for the material and such obvious fondness for Armstrong that his book is a delight to read.