On the norm of a projection onto the space of compact operators

• Autorzy: Joosep Lippus , Eve Oja
• Języki publikacji: EN

Abstrakty

EN

Let X and Y be Banach spaces and let 𝓐(X,Y) be a closed subspace of 𝓛(X,Y), the Banach space of bounded linear operators from X to Y, containing the subspace 𝒦(X,Y) of compact operators. We prove that if Y has the metric compact approximation property and a certain geometric property M*(a,B,c), where a,c ≥ 0 and B is a compact set of scalars (Kalton's property (M*) = M*(1, {-1}, 1)), and if 𝓐(X,Y) ≠ 𝒦(X,Y), then there is no projection from 𝓐(X,Y) onto 𝒦(X,Y) with norm less than max|B| + c. Since, for given λ with 1 < λ < 2, every Y with separable dual can be equivalently renormed to satisfy M*(a,B,c) with max|B| + c = λ, this implies and improves a theorem due to Saphar.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B04: Isometric theory of Banach spaces
• 46B03: Isomorphic theory (including renorming) of Banach 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: 2007
• Tom: 182
• Numer: 3
• Strony: 263-272

Daty

wydano

2007

Twórcy

autor

Joosep Lippus

• Institute of Pure Mathematics, University of Tartu, J. Liivi 2, 50409 Tartu, Estonia

autor

Eve Oja

• Institute of Pure Mathematics, University of Tartu, J. Liivi 2, 50409 Tartu, Estonia

Identyfikatory

DOI

10.4064/sm182-3-5