We prove that every biorthogonality preserving linear surjection from a weakly compact JB*-triple containing no infinite-dimensional rank-one summands onto another JB*-triple is automatically continuous. We also show that every biorthogonality preserving linear surjection between atomic JBW*-triples containing no infinite-dimensional rank-one summands is automatically continuous. Consequently, two atomic JBW*-triples containing no rank-one summands are isomorphic if and only if there exists a (not necessarily continuous) biorthogonality preserving linear surjection between them.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-2-1,
author = {Mar\'\i a Burgos and Jorge J. Garc\'es and Antonio M. Peralta},
title = {Automatic continuity of biorthogonality preservers between weakly compact JB*-triples and atomic JBW*-triples},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {97-121},
zbl = {1234.46055},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-2-1}
}
María Burgos; Jorge J. Garcés; Antonio M. Peralta. Automatic continuity of biorthogonality preservers between weakly compact JB*-triples and atomic JBW*-triples. Studia Mathematica, Tome 204 (2011) pp. 97-121. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-2-1/