The Bishop-Phelps-Bollobás theorem fails for bilinear forms on \(l_{1}\times l_{1}\)

DOI10.1016/J.JMAA.2009.07.008zbMath1190.46012OpenAlexW2090856212MaRDI QIDQ1034595

Hyun Gwi Song, Yun Sung Choi

Publication date: 6 November 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.07.008

zbMATH Keywords

bilinear formBishop-Phelps theoremBishop-Phelps-Bollobás propertynorm attaining operator

Mathematics Subject Classification ID

Isometric theory of Banach spaces (46B04) Forms (bilinear, sesquilinear, multilinear) (47A07) Ideals of polynomials and of multilinear mappings in operator theory (47L22)

Related Items (14)

The Bishop–Phelps–Bollobás Theorem: An Overview ⋮ Bishop-Phelps-Bollobás property for bilinear forms on spaces of continuous functions ⋮ On the Bishop-Phelps-Bollobás theorem for multilinear mappings ⋮ The Bishop-Phelps-Bollobás theorem for operators from \(c_0\) to uniformly convex spaces ⋮ Differentiability of \(L^p\) of a vector measure and applications to the Bishop-Phelps-Bollobás property ⋮ A Bishop-Phelps-Bollobás type theorem for uniform algebras ⋮ On the polynomial Lindenstrauss theorem ⋮ On the Bishop–Phelps–Bollobás property ⋮ Strong subdifferentiability and local Bishop-Phelps-Bollobás properties ⋮ The Bishop-Phelps-Bollobás point property ⋮ The Bishop-Phelps-Bollobás property for bilinear forms and polynomials ⋮ The Bishop-Phelps-Bollobás Theorem for bilinear forms ⋮ The Bishop-Phelps-Bollobás version of Lindenstrauss properties A and B ⋮ The Bishop-Phelps-Bollobás property on the space of \(c_0\)-sum

Cites Work

• The Bishop-Phelps-Bollobás theorem for operators
• Norm attaining operators from \(L_1\) into \(L_\infty\)
• Norm attaining bilinear forms on \(L^ 1[0,1\)]
• A proof that every Banach space is subreflexive
• An Extension to the Theorem of Bishop and Phelps

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