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Duality of the distance to closed operator ideals.
- Source :
- Proceedings of the Royal Society of Edinburgh: Section A: Mathematics; 2002, Vol. 133 Issue 1, p197-212, 16p
- Publication Year :
- 2002
-
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. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 03082105
- Volume :
- 133
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Proceedings of the Royal Society of Edinburgh: Section A: Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 85463371
- Full Text :
- https://doi.org/10.1017/S0308210500002353