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The Bishop-Phelps-Bollobás Theorem for operators from c 0 to uniformly convex spaces

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Abstract

We show that the pair of Banach spaces (c 0, Y) has the Bishop-Phelps-Bollobás property when Y is uniformly convex. Further, when Y is strictly convex, if (c 0, Y) has the Bishop-Phelps-Bollobás property then Y is uniformly convex for the case of real Banach spaces. As a corollary, we show that the Bishop-Phelps-Bollobás theorem holds for bilinear forms on c 0 × ℓ p (1 < p < ∞).

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Authors and Affiliations

  1. School of Mathematics, Korea Institute for Advanced Study (KIAS), 85 Hoegiro, Dongdaemun-gu, Seoul, 130-722, Republic of Korea

    Sun Kwang Kim

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  1. Sun Kwang Kim
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Correspondence to Sun Kwang Kim.

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Kim, S.K. The Bishop-Phelps-Bollobás Theorem for operators from c 0 to uniformly convex spaces. Isr. J. Math. 197, 425–435 (2013). https://doi.org/10.1007/s11856-012-0186-x

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  • DOI: https://doi.org/10.1007/s11856-012-0186-x

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