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On convergence on the boundary of the unit ball in dual space

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Abstract

In this paper some results that are known for extreme points of the unit ball in dual space are carried over to a more general case, namely to the case of the boundary of the ball (Γ ⊂B is the boundary of the unit ballB in the space dual toX if everyx ∈X achieves its maximum value onB at some point of Γ). For example, it is established that if a set is bounded inX and countably compact inσ(X, Γ), then it is weakly compact inX.

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Authors and Affiliations

  1. Tula State Pedagogical University, USSR

    V. I. Rybakov

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  1. V. I. Rybakov
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Translated fromMatematickeskie Zametki, Vol. 59, No. 5, pp. 753–758, May, 1996.

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Rybakov, V.I. On convergence on the boundary of the unit ball in dual space. Math Notes 59, 543–546 (1996). https://doi.org/10.1007/BF02308822

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  • DOI: https://doi.org/10.1007/BF02308822

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