Displaying similar documents to “Decomposable subspaces of Banach spaces.”

Containing l or c and best approximation.

Juan Carlos Cabello Piñar (1990)

Collectanea Mathematica

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The purpose of this paper is to obtain sufficient conditions, for a Banach space X to contain or exclude c0 or l1, in terms of the sets of best approximants in X for the elements in the bidual space.

On subspaces of Banach spaces where every functional has a unique norm-preserving extension

Eve Oja, Märt Põldvere (1996)

Studia Mathematica

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Let X be a Banach space and Y a closed subspace. We obtain simple geometric characterizations of Phelps' property U for Y in X (that every continuous linear functional g ∈ Y* has a unique norm-preserving extension f ∈ X*), which do not use the dual space X*. This enables us to give an intrinsic geometric characterization of preduals of strictly convex spaces close to the Beauzamy-Maurey-Lima-Uttersrud criterion of smoothness. This also enables us to prove that the U-property of the subspace...

Unconditional ideals of finite rank operators

Trond A. Abrahamsen, Asvald Lima, Vegard Lima (2008)

Czechoslovak Mathematical Journal

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Let X be a Banach space. We give characterizations of when ( Y , X ) is a u -ideal in 𝒲 ( Y , X ) for every Banach space Y in terms of nets of finite rank operators approximating weakly compact operators. Similar characterizations are given for the cases when ( X , Y ) is a u -ideal in 𝒲 ( X , Y ) for every Banach space Y , when ( Y , X ) is a u -ideal in 𝒲 ( Y , X * * ) for every Banach space Y , and when ( Y , X ) is a u -ideal in 𝒦 ( Y , X * * ) for every Banach space Y .