Automatic continuity of biorthogonality preservers between weakly compact $JB^*$-triples and atomic $JBW^*$-triples
Studia Mathematica, Tome 204 (2011) no. 2, pp. 97-121
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
prove every biorthogonality preserving linear surjection weakly compact * triple containing infinite dimensional rank one summands another * triple automatically continuous every biorthogonality preserving linear surjection between atomic jbw * triples containing infinite dimensional rank one summands automatically continuous consequently atomic jbw * triples containing rank one summands isomorphic only there exists necessarily continuous biorthogonality preserving linear surjection between
Affiliations des auteurs :
María Burgos 1 ; Jorge J. Garcés 1 ; Antonio M. Peralta 1
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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},
pages = {97--121},
publisher = {mathdoc},
volume = {204},
number = {2},
year = {2011},
doi = {10.4064/sm204-2-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/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) no. 2, pp. 97-121. doi: 10.4064/sm204-2-1
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