On the compact approximation property

• Autorzy: Vegard Lima , Åsvald Lima , Olav Nygaard
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 47L05: Linear spaces of operators
• 46B28: Spaces of operators; tensor products; approximation properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 160
• Numer: 2
• Strony: 185-200

Daty

wydano

2004

Twórcy

autor

Vegard Lima

• Department of Mathematics, Agder University College, Serviceboks 422, 4604 Kristiansand, Norway

autor

Åsvald Lima

• Department of Mathematics, Agder University College, Serviceboks 422, 4604 Kristiansand, Norway

autor

Olav Nygaard

• Department of Mathematics, Agder University College, Serviceboks 422, 4604 Kristiansand, Norway

Identyfikatory

DOI

10.4064/sm160-2-6