Extremal structure of the unit ball of direct sums of Banach spaces

We characterize the extreme points and smooth points of the unit ball of certain direct sums of Banach spaces. We use these results to characterize noncreasiness and uniform noncreasiness of direct sums, thereby extending results of the second author [S. Saejung, Extreme points, smooth points and noncreasiness of ψψ-direct sum of Banach spaces, Nonlinear Anal. 67 (2007) 1649–1653].