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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(lp). This extends a result recently proved by Grząślewicz and Scherwentke whenp = 2 [GS1]. We also show that for any Banach spaceX and for any measure space (Ω, A, μ), the unit ball of ℓ(L 1 (μ), X) has denting points iffL 1(μ) is finite dimensional and the unit ball ofX has a denting point. We also exhibit other classes of Banach spacesX 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.

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Authors and Affiliations

  1. Indian Statistical Institute, R V College Post, 560059, Bangalore, India

    T. S. S. R. K. Rao

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Correspondence to T. S. S. R. K. Rao.

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Rao, T.S.S.R.K. Denting and strongly extreme points in the unit ball of spaces of operators. Proc. Indian Acad. Sci. (Math. Sci.) 109, 75–85 (1999). https://doi.org/10.1007/BF02837769

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  • DOI: https://doi.org/10.1007/BF02837769

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