Currently displaying 1 – 9 of 9

Showing per page

Order by Relevance | Title | Year of publication

Property (wM*) and the unconditional metric compact approximation property

Ăsvald Lima — 1995

Studia Mathematica

The main objective of this paper is to give a simple proof for a larger class of spaces of the following theorem of Kalton and Werner. (a) X has property (M*), and (b) X has the metric compact approximation property Our main tool is a new property (wM*) which we show to be closely related to the unconditional metric approximation property.

Intersection properties of balls in spaces of compact operators

Asvald Lima — 1978

Annales de l'institut Fourier

We study the connection between intersection properties of balls and the existence of large faces of the unit ball in Banach spaces. Hanner’s result that a real space has the 3.2 intersection property if an only if disjoint faces of the unit ball are contained in parallel hyperplanes is extended to infinite dimensional spaces. It is shown that the space of compact operators from a space X to a space Y has the 3.2 intersection property if and only if X and Y have the 3.2 intersection property and...

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

Åsvald Lima;  Eve Oja — 1999

Studia Mathematica

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).

Strict u-ideals in Banach spaces

Vegard Lima;  Åsvald Lima — 2009

Studia Mathematica

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

Vegard Lima;  Åsvald Lima;  Olav Nygaard — 2004

Studia Mathematica

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 = S ∘ T: S compact operator on X is an ideal in = span(,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 s u p γ | | S γ T | | ≤ | | T | | and S γ → I X in the strong operator topology. Similar results for dual spaces are also proved.

Unconditional ideals of finite rank operators

Trond A. Abrahamsen;  Asvald Lima;  Vegard Lima — 2008

Czechoslovak Mathematical Journal

Let X be a Banach space. We give characterizations of when ℱ ( 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 ℱ ( X , Y ) is a u -ideal in 𝒲 ( X , Y ) for every Banach space Y , when ℱ ( Y , X ) is a u -ideal in 𝒲 ( Y , X * * ) for every Banach space Y , and when ℱ ( Y , X ) is a u -ideal in 𝒦 ( Y , X * * ) for every Banach space Y .

Page 1

Download Results (CSV)