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

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## 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 Grząślewicz 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(*L* ^{1} (μ), X) has denting points iff*L* ^{1}(μ) is finite dimensional and the unit ball of*X* has a denting point. We also exhibit other classes of Banach spaces*X* and*Y* 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.

## Keywords

Denting point strongly extreme point*M*-ideal

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© Indian Academy of Sciences 1999