Wyniki wyszukiwania

1

Strict u-ideals in Banach spaces

100%

Lima V., Lima Å.

Studia Mathematica

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2009

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tom 195

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nr 3

275-285

EN

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.

2

Ideals of finite rank operators, intersection properties of balls, and the approximation property

100%

Lima Å., Oja E.

Studia Mathematica

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1999

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tom 133

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nr 2

175-186

EN

We characterize the approximation property of Banach spaces and their dual spaces by the position of finite rank operators in the space of compact operators. In particular, we show that a Banach space E has the approximation property if and only if for all closed subspaces F of $c_0$, the space ℱ(F,E) of finite rank operators from F to E has the n-intersection property in the corresponding space K(F,E) of compact operators for all n, or equivalently, ℱ(F,E) is an ideal in K(F,E).

3

On the compact approximation property

81%

Lima V., Lima Å., Nygaard O.

Studia Mathematica

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2004

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tom 160

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nr 2

185-200

EN

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

3 Studia Mathematica

3 Lima Å.

2 Lima V.

1 Nygaard O.

1 Oja E.

1 2009

1 2004

1 1999

Strict u-ideals in Banach spaces

Ideals of finite rank operators, intersection properties of balls, and the approximation property

On the compact approximation property