Automatic continuity of biorthogonality preservers between weakly compact JB*-triples and atomic JBW*-triples
María Burgos ; Jorge J. Garcés ; Antonio M. Peralta
Studia Mathematica, Tome 204 (2011), p. 97-121 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:285624
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     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},
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     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-2-1}
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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/