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Strict u-ideals in Banach spaces

100%

Lima V., Lima Å.

Studia Mathematica

2009

tom 195

nr 3

275-285

We study strict u-ideals in Banach spaces. A Banach space X is a strict u-ideal in its bidual when the canonical decomposition $X*** = X* ⊕ X^{⊥}$ is unconditional. We characterize Banach spaces which are strict u-ideals in their bidual and show that if X is a strict u-ideal in a Banach space Y then X contains c₀. We also show that $ℓ_{∞}$ is not a u-ideal.

On the compact approximation property

81%

Lima V., Lima Å., Nygaard O.

Studia Mathematica

2004

tom 160

nr 2

185-200

We show that a Banach space X has the compact approximation property if and only if for every Banach space Y and every weakly compact operator T: Y → X, the space 𝔈 = {S ∘ T: S compact operator on X} is an ideal in 𝔉 = span(𝔈,T) if and only if for every Banach space Y and every weakly compact operator T: Y → X, there is a net $(S_γ)$ of compact operators on X such that $sup_{γ}||S_{γ}T|| ≤ ||T||$ and $S_{γ} → I_{X}$ in the strong operator topology. Similar results for dual spaces are also proved.

Ograniczanie wyników

2 Studia Mathematica

2 Lima V.

2 Lima Å.

1 Nygaard O.

1 2009

1 2004

Wyniki wyszukiwania

Strict u-ideals in Banach spaces

On the compact approximation property