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Perturbation of $\ell_1$-copies in Preduals of JBW$^*$-triples

Abstract : Two normal functionals on a JBW$^*$-triple are known to be orthogonal if and only if they are $L$-orthogonal (meaning that they span an isometric copy of $\ell_1(2)$). This is shown to be stable under small norm perturbations in the following sense: if the linear span of the two functionals is isometric up to $\delta>0$ to $\ell_1(2)$, then the functionals are less far (in norm) than $\eps>0$ from two orthogonal functionals, where $\eps\to0$ as $\delta\to0$. Analogous statements for finitely and even infinitely many functionals hold as well. And so does a corresponding statement for non-normal functionals. Our results have been known for C$^*$-algebras.
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  • HAL Id : hal-00993502, version 1
  • ARXIV : 1405.5414

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Antonio Peralta, Hermann Pfitzner. Perturbation of $\ell_1$-copies in Preduals of JBW$^*$-triples. Journal of Mathematical Analysis and Applications, Elsevier, 2016, 434 (1), pp.149-170. ⟨hal-00993502⟩

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