Details

Autor(en) / Beteiligte

• Peralta, Antonio M.
• Pfitzner, Hermann

Titel

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

Ist Teil von

• Journal of mathematical analysis and applications, 2016, Vol.434 (1), p.149-170

Ort / Verlag

Elsevier

Erscheinungsjahr

2016

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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.