Geometry of the Marcinkiewicz sequence space

Abstract

We characterise the real extreme points of the unit ball of mΨ0, the complex extreme points of the unit ball of mΨ and the real extreme and exposed points of the unit ball of (mΨ0)′. Using these characterisations we show that, depending on the length of the extreme points, the multipliers of mΨ0 are either constant multiple of the identity or diagonal operators.