R. Khalil, D. Hussein, W. Amin

Geometry of Modulus Spaces

abstract:
Let f be a modulus function, i.e., continuous strictly increasing function on [0, infinity), such that f (0) = 0, f (1) = 1, and f (x+y) \leq f (x) + f (y) for all x, y in [0, infinity). It is the object of this paper to characterize, for any Banach space X, extreme points, exposed points, and smooth points of the unit ball of the metric linear space l^f(X), the space of all sequences (x_n), x_n in X, n = 1, 2, ... , for which the sum f (||x_n||) is not infinite. Further, extreme, exposed, and smooth points of the unit ball of the space of bounded linear operators on l ^p, 0 < p < 1, are characterized.