Denting and strongly extreme points in the unit ball of spaces of operators

Abstract

For 1 ≤ p ≤ ∞ we show that there are no denting points in the unit ball of L(l^p). This extends a result recently proved by Grzaslewicz and Scherwentke when p = 2 [GS1]. We also show that for any Banach space X and for any measure space (Ω, A, μ ), the unit ball of L(L¹(μ ), X) has denting points iff L¹(μ ) is finite dimensional and the unit ball of X has a denting point. We also exhibit other classes of Banach spaces X andY for which the unit ball of L(X, Y) has no denting points. When X has the extreme point intersection property, we show that all 'nice' operators in the unit ball of L(X, Y) are strongly extreme points.