UO - Université d'Orléans : UMR 7349 (Château de la Source - Avenue du Parc Floral - BP 6749 - 45067 Orléans cedex 2 - France)
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.
https://hal.archives-ouvertes.fr/hal-00993502 Contributor : Hermann PfitznerConnect in order to contact the contributor Submitted on : Wednesday, May 21, 2014 - 11:51:04 AM Last modification on : Wednesday, November 3, 2021 - 6:38:45 AM Long-term archiving on: : Thursday, August 21, 2014 - 10:47:12 AM
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⟩