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Transitivity of proximinality and norm attaining functionals

100%

Narayana D., Rao T.

Colloquium Mathematicum

2006

tom 104

nr 1

1-19

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.

Strongly proximinal subspaces of finite codimension in C(K)

100%

Dutta S., Narayana D.

Colloquium Mathematicum

2007

tom 109

nr 1

119-128

We characterize strongly proximinal subspaces of finite codimension in C(K) spaces. We give two applications of our results. First, we show that the metric projection on a strongly proximinal subspace of finite codimension in C(K) is Hausdorff metric continuous. Second, strong proximinality is a transitive relation for finite-codimensional subspaces of C(K).

Ograniczanie wyników

2 Colloquium Mathematicum

2 Narayana D.

1 Dutta S.

1 Rao T.

1 2007

1 2006

Wyniki wyszukiwania

Transitivity of proximinality and norm attaining functionals

Strongly proximinal subspaces of finite codimension in C(K)