Extreme points, smooth points and noncreasiness of ψψ-direct sum of Banach spaces

Characterizations for noncreasiness and uniform noncreasiness of the ψψ-direct sum of Banach spaces are given. As a consequence, the geometry of the infinite ℓpℓp-direct sum ℓp(Xn)ℓp(Xn) and the Lebesgue–Bochner space Lp(μ,X)Lp(μ,X) with respect to these notions is investigated where 1