Norm attaining bilinear forms on \(L^ 1[0,1]\)

DOI10.1006/jmaa.1997.5461zbMath0888.46007OpenAlexW2050061068MaRDI QIDQ1363562

Yun Sung Choi

Publication date: 14 January 1998

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

Full work available at URL: https://doi.org/10.1006/jmaa.1997.5461

zbMATH Keywords

Dunford-Pettis propertyBishop-Phelps theoremRadon-Nikodym propertymonotone shrinking basisbounded bilinear functionalsnorm attaining bounded bilinear functionalsnorm attaining bounded linear functionals

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Spaces of operators; tensor products; approximation properties (46B28) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Radon-Nikodým, Kre?n-Milman and related properties (46B22)

Related Items (23)

On norm attaining polynomials. ⋮ Norm or numerical radius attaining polynomials on \(C(K\)) ⋮ The Bishop–Phelps–Bollobás Theorem: An Overview ⋮ James type results for polynomials and symmetric multilinear forms ⋮ Bishop-Phelps-Bollobás property for bilinear forms on spaces of continuous functions ⋮ Norm-attaining lattice homomorphisms ⋮ On the Bishop-Phelps-Bollobás theorem for multilinear mappings ⋮ The Bishop-Phelps-Bollobás theorem for operators from \(c_0\) to uniformly convex spaces ⋮ Several remarks on norm attainment in tensor product spaces ⋮ Norm attaining multilinear forms on \(L_{1}(\mu )\) ⋮ Simultaneously continuous retraction and Bishop-Phelps-Bollobás type theorem ⋮ The Bishop-Phelps-Bollobás theorem for operators on \(L_1(\mu)\) ⋮ Polynomials, symmetric multilinear forms and weak compactness ⋮ A multilinear Lindenstrauss theorem ⋮ On the polynomial Lindenstrauss theorem ⋮ Strong subdifferentiability and local Bishop-Phelps-Bollobás properties ⋮ The Bishop-Phelps-Bollobás property for bilinear forms and polynomials ⋮ Extreme polynomials and multilinear forms on \(\ell_1\) ⋮ Norm attaining operators from \(L_1\) into \(L_\infty\) ⋮ Norm-attaining tensors and nuclear operators ⋮ The Bishop-Phelps-Bollobás theorem fails for bilinear forms on \(l_{1}\times l_{1}\) ⋮ Norm Attaining Bilinear Forms on Spaces of Continuous Functions ⋮ Residuality in the set of norm attaining operators between Banach spaces

Cites Work

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• Norm attaining operators on Lebesgue spaces
• Norm attaining operators and renormings of Banach spaces
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• Norm attaining operators on \(L^1[0,1\) and the Radon-Nikodym property]
• There is no bilinear Bishop-Phelps theorem
• On operators which attain their norm
• Symmetric block bases of sequences with large average growth
• A proof that every Banach space is subreflexive
• Norm or Numerical Radius Attaining Multilinear Mappings and Polynomials
• Norm attaining operators

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