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Duality of the distance to closed operator ideals

Published online by Cambridge University Press:  12 July 2007

Hans-Olav Tylli
Hans-Olav Tylli
Affiliation:
Department of Mathematics, PO Box 4 (Yliopistonkatu 5), FIN-00014 University of Helsinki, Finland ([email protected])
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Abstract

Special operator-ideal approximation properties (APs) of Banach spaces are employed to solve the problem of whether the distance functions S ↦ dist(S*, I(F*, E*)) and S ↦ dist(S, I*(E, F)) are uniformly comparable in each space L(E, F) of bounded linear operators. Here, I*(E, F) = {S ∈ L(E, F) : S* ∈ I(F*, E*)} stands for the adjoint ideal of the closed operator ideal I for Banach spaces E and F. Counterexamples are obtained for many classical surjective or injective Banach operator ideals I by solving two resulting ‘asymmetry’ problems for these operator-ideal APs.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 1 , February 2003 , pp. 197 - 212
Copyright
Copyright © Royal Society of Edinburgh 2003

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