Transitivity of proximinality and norm attaining functionals

• Autorzy: Darapaneni Narayana , T. S. S. R. K. Rao
• Języki publikacji: EN

Abstrakty

EN

We study the question of when the set of norm attaining functionals on a Banach space is a linear space. We show that this property is preserved by factor reflexive proximinal subspaces in $\widetilde{R(1)}$ spaces and generally by taking quotients by proximinal subspaces. We show, for 𝒦 (ℓ₂) and c₀-direct sums of families of reflexive spaces, the transitivity of proximinality for factor reflexive subspaces. We also investigate the linear structure of the set of norm attaining functionals on hyperplanes of c₀ and show that, for some particular hyperplanes of c₀, linearity and orthogonal linearity coincide for the set of norm attaining functionals.

Kategorie tematyczne

• 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
• 46B20: Geometry and structure of normed linear spaces
• 41A50: Best approximation, Chebyshev systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 104
• Numer: 1
• Strony: 1-19

Daty

wydano

2006

Twórcy

autor

Darapaneni Narayana

• Department of Mathematics, Indian Institute of Science, Bangalore 560012, India

autor

T. S. S. R. K. Rao

• Stat-Math Unit, Indian Statistical Institute, R. V. College P.O., Bangalore 560059, India

Identyfikatory

DOI

10.4064/cm104-1-1