GEOMETRY OF MODULUS SPACES

Letbe a modulus function, i.e., continuous strictly increasing function on (0;1), such that `(0) = 0, `(1) = 1, and `(x+y) • `(x)+`(y) for all x;y in (0;1). 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 ' ` (X), the space of all sequences (xn), xn 2 X, n = 1;2;:::, for which P `(kxnk) < 1. Further, extreme, exposed, and smooth points of the unit ball of the space of bounded linear operators on ' p , 0 < p < 1; are characterized.