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首页> 外文期刊>Journal of the Mathematical Society of Japan >The Bishop-Phelps-Bollobás property for bilinear forms and polynomials
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The Bishop-Phelps-Bollobás property for bilinear forms and polynomials

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摘要

For a σ-finite measure μ and a Banach space Y we study the Bishop-Phelps-Bollobás property (BPBP) for bilinear forms on L_1(μ)×Y, that is, a (continuous) bilinear form on L_1(μ)×Y almost attaining its norm at (f_0, y_0) can be approximated by bilinear forms attaining their norms at unit vectors close to (f_0, y_0). In case that Y is an Asplund space we characterize the Banach spaces Y satisfying this property. We also exhibit some class of bilinear forms for which the BPBP does not hold, though the set of norm attaining bilinear forms in that class is dense.

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