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

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Lippus J., Oja E.

Studia Mathematica

2007

tom 182

nr 3

263-272

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.

Ograniczanie wyników

1 Studia Mathematica

1 Lippus J.

1 Oja E.

1 2007

Wyniki wyszukiwania

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